Sodium D2 Line

For atoms with hyperfine structure the nuclear spin I is no longer zero so there is coupling between the nuclear magnetic moment of the atom and the angular momentum of the electron cloud. This gives the atom hyperfine stucture.

Aims: * Model Sodium transition (see Farrell 1988 paper - https://doi.org/10.1103/PhysRevA.37.4240) * Compare the Sodium with the paper by Farrell. Do these match exactly?

%run "base-LASED/LASED/laser_atom_system.py"
%run "base-LASED/LASED/time_evolution.py"
%run "base-LASED/LASED/generate_sub_states.py"

import plotly.graph_objects as go
import time

Including Hyperfine Structure

Hyperfine splitting of atomic energy levels is from the coupling of the nuclear-spin (iso-spin) I with the sum of the state’s spin S and orbiatl angular momentum L. This results in a total angular momentum F:

\[F = I + J = I + L + S\]

If an atom has non-zero nuclear spin then the projection of the electron’s angular momentum is \(m_F\). This results in a different coupling between states (different dipole operator matrix element which couple two states together). The coupling between ground state |g> with angular momentum |F’, m\(_F\)> and excited state |e> with angular momentum |F, m\(_F\)> is [Farrell 1995]:

\[\begin{split}C^q_{eg} = (-1)^{1/2(1+q)F+F'+J+J'+I+L+S-m_F+1}\sqrt{(2F+1)(2F'+1)(2J+1)(2J'+1)(2L+1)}\begin{pmatrix} F & 1 & F' \\ -m_F & q &m_F'\end{pmatrix}\begin{Bmatrix}J & F & I \\ F' & J' & 1\end{Bmatrix}\begin{Bmatrix}L & J & S \\ J' & L' & 1\end{Bmatrix}\end{split}\]

where q is the polarisation of the laser radiation: -1 if \(\sigma+\), +1 if \(\sigma-\), and 0 if \(\pi\).

Sodium D\(_2\) Line

In Farrell’s 1988 paper the orange Sodium D\(_2\) line was modelled, specifically the 3\(^2\)S\(_{1/2}\) (F’ = 2) to the 3\(^2\)P\(_{3/2}\) (F = 3,2,1) transition. See Farrell’s paper for the atomic level diagram and information about the hyperfine structure modelling. Farrell also compares the QED approach to the semi-classical (SC) model and shows that the SC model agrees with the QED model at low intensities but the approaches diverge at higher intensities.

The data for the Sodium D line can be found here.

# 3^2S_{1/2} -> 3^2P_{3/2}
wavelength_na = 589.159e-9  # Wavelength in m
w_e = angularFreq(wavelength_na)
tau_na = 16.24  # in ns

I_Na = 3/2  # Isospin for sodium

# Energy Splittings
w1 = 1.77*2*PI # Splitting of 3^2S_{1/2}(F = 1) - (F = 2) in Grad/s
w2 = 0.0158*2*PI  # Splitting between 3^2P_{3/2} (F = 0) and F = 1 in Grad/s
w3 = 0.0355*2*PI  # Splitting between 3^2P_{3/2} (F = 1) and F = 2 in Grad/s
w4 = 0.0595*2*PI  # Splitting between 3^2P_{3/2} (F = 2) and F = 3 in Grad/s

# Detunings
w_Fp1 = -1*w1
w_F0 = w_e-(w4+w3+w2)
w_F1 = w_e-(w4+w3)
w_F2 = w_e-w4
w_F3 = w_e

# Model
# # 3^2S_{1/2} F' = 1
# s1 = State(label = 1, w = 0, m = -1, L = 0, S = 1/2, I = I_Na, F = 1)
Fp1 = generateSubStates(label_from = 1, w = w_Fp1, L = 0, S = 1/2, I = I_Na, F = 1)

# # 3^2S_{1/2} F' = 2
Fp2 = generateSubStates(label_from = 4, w = 0, L = 0, S = 1/2, I = I_Na, F = 2)

# # 3^2P_{3/2} F = 0
# s9 = State(label = 9, w = w_F0, m = 0, L = 1, S = 1/2, I = I_Na, F = 0)
F0 = generateSubStates(label_from = 9, w = w_F0, L = 1, S = 1/2, I = I_Na, F = 0)


# # # 3^2P_{3/2} F = 1
F1 = generateSubStates(label_from = 10, w = w_F1, L = 1, S = 1/2, I = I_Na, F = 1)
# s10 = State(label = 10, w = w_F1, m = -1, L = 1, S = 1/2, I = I_Na, F = 1)


# # # 3^2P_{3/2} F = 2
F2 = generateSubStates(label_from = 13, w = w_F2, L = 1, S = 1/2, I = I_Na, F = 2)
# s13 = State(label = 13, w = w_F2, m = -2, L = 1, S = 1/2, I = I_Na, F = 2)


# # 3^2P_{3/2} F = 3
F3 = generateSubStates(label_from = 18, w = w_F3, L = 1, S = 1/2, I = I_Na, F = 3)

G_na = Fp1 + Fp2
E_na = F0 + F1 + F2 + F3

# Laser parameters
intensity_na = 85.6 # mW/mm^-2
Q_na = [0]
Q_decay = [1, 0, -1]

# Simulation parameters
start_time = 0
stop_time = 500 # in ns
time_steps = 501
time_na = np.linspace(start_time, stop_time, time_steps)

rabi = te.halfRabiFreq(intensity_na, tau_na, wavelength_na)
print(f"rabi = {rabi/np.sqrt(intensity_na)} Grad/s (mW/mm^-2)^-1/2")

for e in E_na:
    for g in G_na:
        for q in Q_na:
            c_eg = te.coupling(e, g, q)
            if(c_eg):
                print( f"C_{e.label},{g.label}^{q} = {c_eg}, rabi = {rabi*c_eg*1000/(np.sqrt(intensity_na)*PI)} Mhz/(mW/mm^-2)")

rabi = 0.0869877402901387 Grad/s (mW/mm^-2)^-1/2
C_9,1^1 = 0.235702260395516*sqrt(6), rabi = 6.52637349073739*sqrt(6) Mhz/(mW/mm^-2)
C_9,2^0 = 0.235702260395516*sqrt(6), rabi = 6.52637349073739*sqrt(6) Mhz/(mW/mm^-2)
C_9,3^-1 = -0.235702260395516*sqrt(6), rabi = -6.52637349073739*sqrt(6) Mhz/(mW/mm^-2)
C_10,1^0 = -0.204124145231931*sqrt(10), rabi = -5.65200523756391*sqrt(10) Mhz/(mW/mm^-2)
C_10,2^-1 = 0.204124145231931*sqrt(10), rabi = 5.65200523756391*sqrt(10) Mhz/(mW/mm^-2)
C_10,4^1 = 0.316227766016838, rabi = 8.75604886310485 Mhz/(mW/mm^-2)
C_10,5^0 = 0.158113883008419*sqrt(2), rabi = 4.37802443155242*sqrt(2) Mhz/(mW/mm^-2)
C_10,6^-1 = -0.052704627669473*sqrt(6), rabi = -1.45934147718414*sqrt(6) Mhz/(mW/mm^-2)
C_11,1^1 = 0.204124145231931*sqrt(10), rabi = 5.65200523756391*sqrt(10) Mhz/(mW/mm^-2)
C_11,3^-1 = 0.204124145231931*sqrt(10), rabi = 5.65200523756391*sqrt(10) Mhz/(mW/mm^-2)
C_11,5^1 = 0.158113883008419*sqrt(2), rabi = 4.37802443155242*sqrt(2) Mhz/(mW/mm^-2)
C_11,6^0 = 0.105409255338946*sqrt(6), rabi = 2.91868295436828*sqrt(6) Mhz/(mW/mm^-2)
C_11,7^-1 = -0.158113883008419*sqrt(2), rabi = -4.37802443155242*sqrt(2) Mhz/(mW/mm^-2)
C_12,2^1 = 0.204124145231931*sqrt(10), rabi = 5.65200523756391*sqrt(10) Mhz/(mW/mm^-2)
C_12,3^0 = 0.204124145231931*sqrt(10), rabi = 5.65200523756391*sqrt(10) Mhz/(mW/mm^-2)
C_12,6^1 = 0.052704627669473*sqrt(6), rabi = 1.45934147718414*sqrt(6) Mhz/(mW/mm^-2)
C_12,7^0 = 0.158113883008419*sqrt(2), rabi = 4.37802443155242*sqrt(2) Mhz/(mW/mm^-2)
C_12,8^-1 = -0.316227766016838, rabi = -8.75604886310485 Mhz/(mW/mm^-2)
C_13,1^-1 = -0.316227766016838*sqrt(5), rabi = -8.75604886310485*sqrt(5) Mhz/(mW/mm^-2)
C_13,4^0 = -0.408248290463863*sqrt(2), rabi = -11.3040104751278*sqrt(2) Mhz/(mW/mm^-2)
C_13,5^-1 = 0.408248290463863, rabi = 11.3040104751278 Mhz/(mW/mm^-2)
C_14,1^0 = -0.158113883008419*sqrt(10), rabi = -4.37802443155242*sqrt(10) Mhz/(mW/mm^-2)
C_14,2^-1 = -0.158113883008419*sqrt(10), rabi = -4.37802443155242*sqrt(10) Mhz/(mW/mm^-2)
C_14,4^1 = 0.408248290463863, rabi = 11.3040104751278 Mhz/(mW/mm^-2)
C_14,5^0 = -0.204124145231932*sqrt(2), rabi = -5.65200523756391*sqrt(2) Mhz/(mW/mm^-2)
C_14,6^-1 = 0.204124145231932*sqrt(6), rabi = 5.65200523756391*sqrt(6) Mhz/(mW/mm^-2)
C_15,1^1 = 0.052704627669473*sqrt(30), rabi = 1.45934147718414*sqrt(30) Mhz/(mW/mm^-2)
C_15,2^0 = -0.105409255338946*sqrt(30), rabi = -2.91868295436828*sqrt(30) Mhz/(mW/mm^-2)
C_15,3^-1 = -0.052704627669473*sqrt(30), rabi = -1.45934147718414*sqrt(30) Mhz/(mW/mm^-2)
C_15,5^1 = 0.204124145231932*sqrt(6), rabi = 5.65200523756391*sqrt(6) Mhz/(mW/mm^-2)
C_15,7^-1 = 0.204124145231932*sqrt(6), rabi = 5.65200523756391*sqrt(6) Mhz/(mW/mm^-2)
C_16,2^1 = 0.158113883008419*sqrt(10), rabi = 4.37802443155242*sqrt(10) Mhz/(mW/mm^-2)
C_16,3^0 = -0.158113883008419*sqrt(10), rabi = -4.37802443155242*sqrt(10) Mhz/(mW/mm^-2)
C_16,6^1 = 0.204124145231932*sqrt(6), rabi = 5.65200523756391*sqrt(6) Mhz/(mW/mm^-2)
C_16,7^0 = 0.204124145231932*sqrt(2), rabi = 5.65200523756391*sqrt(2) Mhz/(mW/mm^-2)
C_16,8^-1 = 0.408248290463863, rabi = 11.3040104751278 Mhz/(mW/mm^-2)
C_17,3^1 = 0.316227766016838*sqrt(5), rabi = 8.75604886310485*sqrt(5) Mhz/(mW/mm^-2)
C_17,7^1 = 0.408248290463863, rabi = 11.3040104751278 Mhz/(mW/mm^-2)
C_17,8^0 = 0.408248290463863*sqrt(2), rabi = 11.3040104751278*sqrt(2) Mhz/(mW/mm^-2)
C_18,4^-1 = -0.0690065559342354*sqrt(210), rabi = -1.91072650971*sqrt(210) Mhz/(mW/mm^-2)
C_19,4^0 = -0.0690065559342354*sqrt(70), rabi = -1.91072650971*sqrt(70) Mhz/(mW/mm^-2)
C_19,5^-1 = -0.138013111868471*sqrt(35), rabi = -3.82145301942*sqrt(35) Mhz/(mW/mm^-2)
C_20,4^1 = 0.0690065559342354*sqrt(14), rabi = 1.91072650971*sqrt(14) Mhz/(mW/mm^-2)
C_20,5^0 = -0.276026223736942*sqrt(7), rabi = -7.64290603884*sqrt(7) Mhz/(mW/mm^-2)
C_20,6^-1 = -0.138013111868471*sqrt(21), rabi = -3.82145301942*sqrt(21) Mhz/(mW/mm^-2)
C_21,5^1 = 0.0690065559342354*sqrt(42), rabi = 1.91072650971*sqrt(42) Mhz/(mW/mm^-2)
C_21,6^0 = -0.207019667802706*sqrt(14), rabi = -5.73217952913*sqrt(14) Mhz/(mW/mm^-2)
C_21,7^-1 = -0.0690065559342354*sqrt(42), rabi = -1.91072650971*sqrt(42) Mhz/(mW/mm^-2)
C_22,6^1 = 0.138013111868471*sqrt(21), rabi = 3.82145301942*sqrt(21) Mhz/(mW/mm^-2)
C_22,7^0 = -0.276026223736942*sqrt(7), rabi = -7.64290603884*sqrt(7) Mhz/(mW/mm^-2)
C_22,8^-1 = -0.0690065559342354*sqrt(14), rabi = -1.91072650971*sqrt(14) Mhz/(mW/mm^-2)
C_23,7^1 = 0.138013111868471*sqrt(35), rabi = 3.82145301942*sqrt(35) Mhz/(mW/mm^-2)
C_23,8^0 = -0.0690065559342354*sqrt(70), rabi = -1.91072650971*sqrt(70) Mhz/(mW/mm^-2)
C_24,8^1 = 0.0690065559342354*sqrt(210), rabi = 1.91072650971*sqrt(210) Mhz/(mW/mm^-2)

sodium_system = LaserAtomSystem(E_na, G_na, tau_na, Q_na, wavelength_na,
                                 laser_intensity = intensity_na)
tic = time.perf_counter()
sodium_system.timeEvolution(time_na, pretty_print_eq = True)
toc = time.perf_counter()
print(f"The code finished in {toc-tic:0.4f} seconds")

Populating ground states equally as the initial condition.

$\displaystyle \dot{\rho}_{11} = - i \rho_{101} \Omega{\left(10,1,0 \right)} + \frac{0.416666666666667 \rho_{1010}}{\tau} + \frac{0.322748612183951 \rho_{1014}}{\tau} + i \rho_{110} \Omega{\left(10,1,0 \right)} + \frac{0.416666666666667 \rho_{1111}}{\tau} + \frac{0.186338998124982 \rho_{1115}}{\tau} + i \rho_{114} \Omega{\left(14,1,0 \right)} + \frac{0.372677996249965 \rho_{119}}{\tau} + \frac{0.5 \rho_{1313}}{\tau} - i \rho_{141} \Omega{\left(14,1,0 \right)} + \frac{0.322748612183951 \rho_{1410}}{\tau} + \frac{0.25 \rho_{1414}}{\tau} + \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.0833333333333333 \rho_{1515}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} + \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau} + \frac{0.333333333333333 \rho_{99}}{\tau}$

$\displaystyle \dot{\rho}_{12} = - \frac{0.322748612183951 \rho_{1014}}{\tau} - i \rho_{102} \Omega{\left(10,1,0 \right)} + i \rho_{115} \Omega{\left(15,2,0 \right)} + \frac{0.322748612183951 \rho_{1216}}{\tau} - \frac{0.322748612183951 \rho_{1410}}{\tau} - i \rho_{142} \Omega{\left(14,1,0 \right)} - \frac{0.333333333333333 \rho_{159}}{\tau} + \frac{0.322748612183951 \rho_{1612}}{\tau} + i \rho_{19} \Omega{\left(9,2,0 \right)} - \frac{0.333333333333333 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{13} = - i \rho_{103} \Omega{\left(10,1,0 \right)} - \frac{0.186338998124982 \rho_{1115}}{\tau} + i \rho_{112} \Omega{\left(12,3,0 \right)} + i \rho_{116} \Omega{\left(16,3,0 \right)} - \frac{0.372677996249965 \rho_{119}}{\tau} - \frac{0.322748612183951 \rho_{1216}}{\tau} - i \rho_{143} \Omega{\left(14,1,0 \right)} - \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - \frac{0.322748612183951 \rho_{1612}}{\tau} - \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{14} = \Delta_{14} \rho_{14} + \frac{0.129099444873581 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - i \rho_{104} \Omega{\left(10,1,0 \right)} + i \rho_{113} \Omega{\left(13,4,0 \right)} + i \rho_{119} \Omega{\left(19,4,0 \right)} + \frac{0.333333333333333 \rho_{1319}}{\tau} + \frac{0.129099444873581 \rho_{1410}}{\tau} + \frac{0.105409255338946 \rho_{1420}}{\tau} - i \rho_{144} \Omega{\left(14,1,0 \right)} + \frac{0.333333333333333 \rho_{1913}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} + \frac{0.105409255338946 \rho_{2014}}{\tau}$

$\displaystyle \dot{\rho}_{15} = \Delta_{15} \rho_{15} + \frac{0.0645497224367903 \sqrt{5} \rho_{1010}}{\tau} - \frac{0.0645497224367903 \rho_{1014}}{\tau} - \frac{0.163299316185545 \rho_{1020}}{\tau} - i \rho_{105} \Omega{\left(10,1,0 \right)} + i \rho_{110} \Omega{\left(10,5,0 \right)} + \frac{0.0645497224367903 \sqrt{5} \rho_{1111}}{\tau} + \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} + i \rho_{114} \Omega{\left(14,5,0 \right)} + i \rho_{120} \Omega{\left(20,5,0 \right)} + \frac{0.129099444873581 \sqrt{5} \rho_{1313}}{\tau} - \frac{0.333333333333333 \rho_{1319}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1414}}{\tau} + \frac{0.210818510677892 \rho_{1420}}{\tau} - i \rho_{145} \Omega{\left(14,1,0 \right)} + \frac{0.11180339887499 \rho_{1511}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1515}}{\tau} + \frac{0.223606797749979 \rho_{1521}}{\tau} - \frac{0.333333333333333 \rho_{1913}}{\tau} - \frac{0.163299316185545 \rho_{2010}}{\tau} + \frac{0.210818510677892 \rho_{2014}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} + \frac{0.223606797749979 \rho_{2115}}{\tau}$

$\displaystyle \dot{\rho}_{16} = \Delta_{16} \rho_{16} - \frac{0.0645497224367903 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - i \rho_{106} \Omega{\left(10,1,0 \right)} + i \rho_{111} \Omega{\left(11,6,0 \right)} - \frac{0.2 \rho_{1121}}{\tau} + i \rho_{121} \Omega{\left(21,6,0 \right)} + \frac{0.0645497224367903 \rho_{1216}}{\tau} + \frac{0.0816496580927726 \rho_{1222}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} - \frac{0.316227766016838 \rho_{1420}}{\tau} - i \rho_{146} \Omega{\left(14,1,0 \right)} + \frac{0.0645497224367903 \rho_{1612}}{\tau} + \frac{0.316227766016838 \rho_{1622}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} - \frac{0.316227766016838 \rho_{2014}}{\tau} - \frac{0.2 \rho_{2111}}{\tau} + \frac{0.0816496580927726 \rho_{2212}}{\tau} + \frac{0.316227766016838 \rho_{2216}}{\tau}$

$\displaystyle \dot{\rho}_{17} = \Delta_{17} \rho_{17} - i \rho_{107} \Omega{\left(10,1,0 \right)} - \frac{0.11180339887499 \rho_{1115}}{\tau} + i \rho_{112} \Omega{\left(12,7,0 \right)} + \frac{0.1 \rho_{1121}}{\tau} + i \rho_{116} \Omega{\left(16,7,0 \right)} + \frac{0.0645497224367903 \rho_{1216}}{\tau} + i \rho_{122} \Omega{\left(22,7,0 \right)} - \frac{0.163299316185545 \rho_{1222}}{\tau} - i \rho_{147} \Omega{\left(14,1,0 \right)} - \frac{0.11180339887499 \rho_{1511}}{\tau} - \frac{0.223606797749979 \rho_{1521}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} - \frac{0.210818510677892 \rho_{1622}}{\tau} + \frac{0.333333333333333 \rho_{1723}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} - \frac{0.223606797749979 \rho_{2115}}{\tau} - \frac{0.163299316185545 \rho_{2212}}{\tau} - \frac{0.210818510677892 \rho_{2216}}{\tau} + \frac{0.333333333333333 \rho_{2317}}{\tau}$

$\displaystyle \dot{\rho}_{18} = \Delta_{18} \rho_{18} - i \rho_{108} \Omega{\left(10,1,0 \right)} + i \rho_{117} \Omega{\left(17,8,0 \right)} - \frac{0.129099444873581 \rho_{1216}}{\tau} + \frac{0.0816496580927727 \rho_{1222}}{\tau} + i \rho_{123} \Omega{\left(23,8,0 \right)} - i \rho_{148} \Omega{\left(14,1,0 \right)} - \frac{0.129099444873581 \rho_{1612}}{\tau} - \frac{0.105409255338946 \rho_{1622}}{\tau} - \frac{0.333333333333333 \rho_{1723}}{\tau} + \frac{0.0816496580927727 \rho_{2212}}{\tau} - \frac{0.105409255338946 \rho_{2216}}{\tau} - \frac{0.333333333333333 \rho_{2317}}{\tau}$

$\displaystyle \dot{\rho}_{21} = \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.186338998124982 \rho_{1115}}{\tau} + \frac{0.372677996249965 \rho_{119}}{\tau} + \frac{0.322748612183951 \rho_{1410}}{\tau} - i \rho_{151} \Omega{\left(15,2,0 \right)} + \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} + i \rho_{210} \Omega{\left(10,1,0 \right)} + i \rho_{214} \Omega{\left(14,1,0 \right)} - i \rho_{91} \Omega{\left(9,2,0 \right)} + \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{22} = \frac{0.416666666666667 \rho_{1010}}{\tau} - \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.416666666666667 \rho_{1212}}{\tau} + \frac{0.322748612183951 \rho_{1216}}{\tau} - \frac{0.322748612183951 \rho_{1410}}{\tau} + \frac{0.25 \rho_{1414}}{\tau} + \frac{0.333333333333333 \rho_{1515}}{\tau} - i \rho_{152} \Omega{\left(15,2,0 \right)} - \frac{0.333333333333333 \rho_{159}}{\tau} + \frac{0.322748612183951 \rho_{1612}}{\tau} + \frac{0.25 \rho_{1616}}{\tau} + i \rho_{215} \Omega{\left(15,2,0 \right)} + i \rho_{29} \Omega{\left(9,2,0 \right)} - \frac{0.333333333333333 \rho_{915}}{\tau} - i \rho_{92} \Omega{\left(9,2,0 \right)} + \frac{0.333333333333333 \rho_{99}}{\tau}$

$\displaystyle \dot{\rho}_{23} = - \frac{0.186338998124982 \rho_{1115}}{\tau} - \frac{0.372677996249965 \rho_{119}}{\tau} - \frac{0.322748612183951 \rho_{1216}}{\tau} - \frac{0.186338998124982 \rho_{1511}}{\tau} - i \rho_{153} \Omega{\left(15,2,0 \right)} + \frac{0.166666666666667 \rho_{159}}{\tau} - \frac{0.322748612183951 \rho_{1612}}{\tau} + i \rho_{212} \Omega{\left(12,3,0 \right)} + i \rho_{216} \Omega{\left(16,3,0 \right)} - \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau} - i \rho_{93} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{24} = \Delta_{24} \rho_{24} + \frac{0.129099444873581 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} + \frac{0.333333333333333 \rho_{1319}}{\tau} + \frac{0.129099444873581 \rho_{1410}}{\tau} + \frac{0.105409255338946 \rho_{1420}}{\tau} - i \rho_{154} \Omega{\left(15,2,0 \right)} + \frac{0.333333333333333 \rho_{1913}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} + \frac{0.105409255338946 \rho_{2014}}{\tau} + i \rho_{213} \Omega{\left(13,4,0 \right)} + i \rho_{219} \Omega{\left(19,4,0 \right)} - i \rho_{94} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{25} = \Delta_{25} \rho_{25} - \frac{0.0645497224367903 \rho_{1014}}{\tau} - \frac{0.163299316185545 \rho_{1020}}{\tau} + \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} - \frac{0.333333333333333 \rho_{1319}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} + \frac{0.210818510677892 \rho_{1420}}{\tau} + \frac{0.11180339887499 \rho_{1511}}{\tau} + \frac{0.223606797749979 \rho_{1521}}{\tau} - i \rho_{155} \Omega{\left(15,2,0 \right)} - \frac{0.333333333333333 \rho_{1913}}{\tau} - \frac{0.163299316185545 \rho_{2010}}{\tau} + \frac{0.210818510677892 \rho_{2014}}{\tau} + i \rho_{210} \Omega{\left(10,5,0 \right)} + \frac{0.1 \rho_{2111}}{\tau} + \frac{0.223606797749979 \rho_{2115}}{\tau} + i \rho_{214} \Omega{\left(14,5,0 \right)} + i \rho_{220} \Omega{\left(20,5,0 \right)} - i \rho_{95} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{26} = \Delta_{26} \rho_{26} + \frac{0.0215165741455968 \sqrt{15} \rho_{1010}}{\tau} - \frac{0.0645497224367903 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - \frac{0.2 \rho_{1121}}{\tau} + \frac{0.0215165741455968 \sqrt{15} \rho_{1212}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} + \frac{0.0816496580927726 \rho_{1222}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} + \frac{0.0645497224367903 \sqrt{15} \rho_{1414}}{\tau} - \frac{0.316227766016838 \rho_{1420}}{\tau} - i \rho_{156} \Omega{\left(15,2,0 \right)} + \frac{0.0645497224367903 \rho_{1612}}{\tau} + \frac{0.0645497224367903 \sqrt{15} \rho_{1616}}{\tau} + \frac{0.316227766016838 \rho_{1622}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} - \frac{0.316227766016838 \rho_{2014}}{\tau} + i \rho_{211} \Omega{\left(11,6,0 \right)} - \frac{0.2 \rho_{2111}}{\tau} + i \rho_{221} \Omega{\left(21,6,0 \right)} + \frac{0.0816496580927726 \rho_{2212}}{\tau} + \frac{0.316227766016838 \rho_{2216}}{\tau} - i \rho_{96} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{27} = \Delta_{27} \rho_{27} - \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} - \frac{0.163299316185545 \rho_{1222}}{\tau} - \frac{0.11180339887499 \rho_{1511}}{\tau} - \frac{0.223606797749979 \rho_{1521}}{\tau} - i \rho_{157} \Omega{\left(15,2,0 \right)} + \frac{0.0645497224367903 \rho_{1612}}{\tau} - \frac{0.210818510677892 \rho_{1622}}{\tau} + \frac{0.333333333333333 \rho_{1723}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} - \frac{0.223606797749979 \rho_{2115}}{\tau} + i \rho_{212} \Omega{\left(12,7,0 \right)} + i \rho_{216} \Omega{\left(16,7,0 \right)} - \frac{0.163299316185545 \rho_{2212}}{\tau} - \frac{0.210818510677892 \rho_{2216}}{\tau} + i \rho_{222} \Omega{\left(22,7,0 \right)} + \frac{0.333333333333333 \rho_{2317}}{\tau} - i \rho_{97} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{28} = \Delta_{28} \rho_{28} - \frac{0.129099444873581 \rho_{1216}}{\tau} + \frac{0.0816496580927727 \rho_{1222}}{\tau} - i \rho_{158} \Omega{\left(15,2,0 \right)} - \frac{0.129099444873581 \rho_{1612}}{\tau} - \frac{0.105409255338946 \rho_{1622}}{\tau} - \frac{0.333333333333333 \rho_{1723}}{\tau} + i \rho_{217} \Omega{\left(17,8,0 \right)} + \frac{0.0816496580927727 \rho_{2212}}{\tau} - \frac{0.105409255338946 \rho_{2216}}{\tau} + i \rho_{223} \Omega{\left(23,8,0 \right)} - \frac{0.333333333333333 \rho_{2317}}{\tau} - i \rho_{98} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{31} = \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.186338998124982 \rho_{1115}}{\tau} + \frac{0.372677996249965 \rho_{119}}{\tau} - i \rho_{121} \Omega{\left(12,3,0 \right)} + \frac{0.322748612183951 \rho_{1410}}{\tau} + \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - i \rho_{161} \Omega{\left(16,3,0 \right)} + i \rho_{310} \Omega{\left(10,1,0 \right)} + i \rho_{314} \Omega{\left(14,1,0 \right)} + \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{32} = - \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.322748612183951 \rho_{1216}}{\tau} - i \rho_{122} \Omega{\left(12,3,0 \right)} - \frac{0.322748612183951 \rho_{1410}}{\tau} - \frac{0.333333333333333 \rho_{159}}{\tau} + \frac{0.322748612183951 \rho_{1612}}{\tau} - i \rho_{162} \Omega{\left(16,3,0 \right)} + i \rho_{315} \Omega{\left(15,2,0 \right)} + i \rho_{39} \Omega{\left(9,2,0 \right)} - \frac{0.333333333333333 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{33} = \frac{0.416666666666667 \rho_{1111}}{\tau} - \frac{0.186338998124982 \rho_{1115}}{\tau} - \frac{0.372677996249965 \rho_{119}}{\tau} + \frac{0.416666666666667 \rho_{1212}}{\tau} - \frac{0.322748612183951 \rho_{1216}}{\tau} - i \rho_{123} \Omega{\left(12,3,0 \right)} - \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.0833333333333333 \rho_{1515}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - \frac{0.322748612183951 \rho_{1612}}{\tau} + \frac{0.25 \rho_{1616}}{\tau} - i \rho_{163} \Omega{\left(16,3,0 \right)} + \frac{0.5 \rho_{1717}}{\tau} + i \rho_{312} \Omega{\left(12,3,0 \right)} + i \rho_{316} \Omega{\left(16,3,0 \right)} - \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau} + \frac{0.333333333333333 \rho_{99}}{\tau}$

$\displaystyle \dot{\rho}_{34} = \Delta_{34} \rho_{34} + \frac{0.129099444873581 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - i \rho_{124} \Omega{\left(12,3,0 \right)} + \frac{0.333333333333333 \rho_{1319}}{\tau} + \frac{0.129099444873581 \rho_{1410}}{\tau} + \frac{0.105409255338946 \rho_{1420}}{\tau} - i \rho_{164} \Omega{\left(16,3,0 \right)} + \frac{0.333333333333333 \rho_{1913}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} + \frac{0.105409255338946 \rho_{2014}}{\tau} + i \rho_{313} \Omega{\left(13,4,0 \right)} + i \rho_{319} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{35} = \Delta_{35} \rho_{35} - \frac{0.0645497224367903 \rho_{1014}}{\tau} - \frac{0.163299316185545 \rho_{1020}}{\tau} + \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} - i \rho_{125} \Omega{\left(12,3,0 \right)} - \frac{0.333333333333333 \rho_{1319}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} + \frac{0.210818510677892 \rho_{1420}}{\tau} + \frac{0.11180339887499 \rho_{1511}}{\tau} + \frac{0.223606797749979 \rho_{1521}}{\tau} - i \rho_{165} \Omega{\left(16,3,0 \right)} - \frac{0.333333333333333 \rho_{1913}}{\tau} - \frac{0.163299316185545 \rho_{2010}}{\tau} + \frac{0.210818510677892 \rho_{2014}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} + \frac{0.223606797749979 \rho_{2115}}{\tau} + i \rho_{310} \Omega{\left(10,5,0 \right)} + i \rho_{314} \Omega{\left(14,5,0 \right)} + i \rho_{320} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{36} = \Delta_{36} \rho_{36} - \frac{0.0645497224367903 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - \frac{0.2 \rho_{1121}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} + \frac{0.0816496580927726 \rho_{1222}}{\tau} - i \rho_{126} \Omega{\left(12,3,0 \right)} - \frac{0.0645497224367903 \rho_{1410}}{\tau} - \frac{0.316227766016838 \rho_{1420}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} + \frac{0.316227766016838 \rho_{1622}}{\tau} - i \rho_{166} \Omega{\left(16,3,0 \right)} + \frac{0.0816496580927726 \rho_{2010}}{\tau} - \frac{0.316227766016838 \rho_{2014}}{\tau} - \frac{0.2 \rho_{2111}}{\tau} + \frac{0.0816496580927726 \rho_{2212}}{\tau} + \frac{0.316227766016838 \rho_{2216}}{\tau} + i \rho_{311} \Omega{\left(11,6,0 \right)} + i \rho_{321} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{37} = \Delta_{37} \rho_{37} + \frac{0.0645497224367903 \sqrt{5} \rho_{1111}}{\tau} - \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1212}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} - \frac{0.163299316185545 \rho_{1222}}{\tau} - i \rho_{127} \Omega{\left(12,3,0 \right)} - \frac{0.11180339887499 \rho_{1511}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1515}}{\tau} - \frac{0.223606797749979 \rho_{1521}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1616}}{\tau} - \frac{0.210818510677892 \rho_{1622}}{\tau} - i \rho_{167} \Omega{\left(16,3,0 \right)} + \frac{0.129099444873581 \sqrt{5} \rho_{1717}}{\tau} + \frac{0.333333333333333 \rho_{1723}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} - \frac{0.223606797749979 \rho_{2115}}{\tau} - \frac{0.163299316185545 \rho_{2212}}{\tau} - \frac{0.210818510677892 \rho_{2216}}{\tau} + \frac{0.333333333333333 \rho_{2317}}{\tau} + i \rho_{312} \Omega{\left(12,7,0 \right)} + i \rho_{316} \Omega{\left(16,7,0 \right)} + i \rho_{322} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{38} = \Delta_{38} \rho_{38} - \frac{0.129099444873581 \rho_{1216}}{\tau} + \frac{0.0816496580927727 \rho_{1222}}{\tau} - i \rho_{128} \Omega{\left(12,3,0 \right)} - \frac{0.129099444873581 \rho_{1612}}{\tau} - \frac{0.105409255338946 \rho_{1622}}{\tau} - i \rho_{168} \Omega{\left(16,3,0 \right)} - \frac{0.333333333333333 \rho_{1723}}{\tau} + \frac{0.0816496580927727 \rho_{2212}}{\tau} - \frac{0.105409255338946 \rho_{2216}}{\tau} - \frac{0.333333333333333 \rho_{2317}}{\tau} + i \rho_{317} \Omega{\left(17,8,0 \right)} + i \rho_{323} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{41} = \Delta_{41} \rho_{41} + \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.186338998124982 \rho_{1115}}{\tau} + \frac{0.372677996249965 \rho_{119}}{\tau} - i \rho_{131} \Omega{\left(13,4,0 \right)} + \frac{0.322748612183951 \rho_{1410}}{\tau} + \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - i \rho_{191} \Omega{\left(19,4,0 \right)} + i \rho_{410} \Omega{\left(10,1,0 \right)} + i \rho_{414} \Omega{\left(14,1,0 \right)} + \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{42} = \Delta_{42} \rho_{42} - \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.322748612183951 \rho_{1216}}{\tau} - i \rho_{132} \Omega{\left(13,4,0 \right)} - \frac{0.322748612183951 \rho_{1410}}{\tau} - \frac{0.333333333333333 \rho_{159}}{\tau} + \frac{0.322748612183951 \rho_{1612}}{\tau} - i \rho_{192} \Omega{\left(19,4,0 \right)} + i \rho_{415} \Omega{\left(15,2,0 \right)} + i \rho_{49} \Omega{\left(9,2,0 \right)} - \frac{0.333333333333333 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{43} = \Delta_{43} \rho_{43} - \frac{0.186338998124982 \rho_{1115}}{\tau} - \frac{0.372677996249965 \rho_{119}}{\tau} - \frac{0.322748612183951 \rho_{1216}}{\tau} - i \rho_{133} \Omega{\left(13,4,0 \right)} - \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - \frac{0.322748612183951 \rho_{1612}}{\tau} - i \rho_{193} \Omega{\left(19,4,0 \right)} + i \rho_{412} \Omega{\left(12,3,0 \right)} + i \rho_{416} \Omega{\left(16,3,0 \right)} - \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{44} = \frac{0.1 \rho_{1010}}{\tau} + \frac{0.129099444873581 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} + \frac{0.333333333333333 \rho_{1313}}{\tau} + \frac{0.333333333333333 \rho_{1319}}{\tau} - i \rho_{134} \Omega{\left(13,4,0 \right)} + \frac{0.129099444873581 \rho_{1410}}{\tau} + \frac{0.166666666666667 \rho_{1414}}{\tau} + \frac{0.105409255338946 \rho_{1420}}{\tau} + \frac{1.0 \rho_{1818}}{\tau} + \frac{0.333333333333333 \rho_{1913}}{\tau} + \frac{0.333333333333333 \rho_{1919}}{\tau} - i \rho_{194} \Omega{\left(19,4,0 \right)} + \frac{0.0816496580927726 \rho_{2010}}{\tau} + \frac{0.105409255338946 \rho_{2014}}{\tau} + \frac{0.0666666666666667 \rho_{2020}}{\tau} + i \rho_{413} \Omega{\left(13,4,0 \right)} + i \rho_{419} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{45} = - \frac{0.0645497224367903 \rho_{1014}}{\tau} - \frac{0.163299316185545 \rho_{1020}}{\tau} + \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} - \frac{0.333333333333333 \rho_{1319}}{\tau} - i \rho_{135} \Omega{\left(13,4,0 \right)} - \frac{0.0645497224367903 \rho_{1410}}{\tau} + \frac{0.210818510677892 \rho_{1420}}{\tau} + \frac{0.11180339887499 \rho_{1511}}{\tau} + \frac{0.223606797749979 \rho_{1521}}{\tau} - \frac{0.333333333333333 \rho_{1913}}{\tau} - i \rho_{195} \Omega{\left(19,4,0 \right)} - \frac{0.163299316185545 \rho_{2010}}{\tau} + \frac{0.210818510677892 \rho_{2014}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} + \frac{0.223606797749979 \rho_{2115}}{\tau} + i \rho_{410} \Omega{\left(10,5,0 \right)} + i \rho_{414} \Omega{\left(14,5,0 \right)} + i \rho_{420} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{46} = - \frac{0.0645497224367903 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - \frac{0.2 \rho_{1121}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} + \frac{0.0816496580927726 \rho_{1222}}{\tau} - i \rho_{136} \Omega{\left(13,4,0 \right)} - \frac{0.0645497224367903 \rho_{1410}}{\tau} - \frac{0.316227766016838 \rho_{1420}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} + \frac{0.316227766016838 \rho_{1622}}{\tau} - i \rho_{196} \Omega{\left(19,4,0 \right)} + \frac{0.0816496580927726 \rho_{2010}}{\tau} - \frac{0.316227766016838 \rho_{2014}}{\tau} - \frac{0.2 \rho_{2111}}{\tau} + \frac{0.0816496580927726 \rho_{2212}}{\tau} + \frac{0.316227766016838 \rho_{2216}}{\tau} + i \rho_{411} \Omega{\left(11,6,0 \right)} + i \rho_{421} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{47} = - \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} - \frac{0.163299316185545 \rho_{1222}}{\tau} - i \rho_{137} \Omega{\left(13,4,0 \right)} - \frac{0.11180339887499 \rho_{1511}}{\tau} - \frac{0.223606797749979 \rho_{1521}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} - \frac{0.210818510677892 \rho_{1622}}{\tau} + \frac{0.333333333333333 \rho_{1723}}{\tau} - i \rho_{197} \Omega{\left(19,4,0 \right)} + \frac{0.1 \rho_{2111}}{\tau} - \frac{0.223606797749979 \rho_{2115}}{\tau} - \frac{0.163299316185545 \rho_{2212}}{\tau} - \frac{0.210818510677892 \rho_{2216}}{\tau} + \frac{0.333333333333333 \rho_{2317}}{\tau} + i \rho_{412} \Omega{\left(12,7,0 \right)} + i \rho_{416} \Omega{\left(16,7,0 \right)} + i \rho_{422} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{48} = - \frac{0.129099444873581 \rho_{1216}}{\tau} + \frac{0.0816496580927727 \rho_{1222}}{\tau} - i \rho_{138} \Omega{\left(13,4,0 \right)} - \frac{0.129099444873581 \rho_{1612}}{\tau} - \frac{0.105409255338946 \rho_{1622}}{\tau} - \frac{0.333333333333333 \rho_{1723}}{\tau} - i \rho_{198} \Omega{\left(19,4,0 \right)} + \frac{0.0816496580927727 \rho_{2212}}{\tau} - \frac{0.105409255338946 \rho_{2216}}{\tau} - \frac{0.333333333333333 \rho_{2317}}{\tau} + i \rho_{417} \Omega{\left(17,8,0 \right)} + i \rho_{423} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{51} = \Delta_{51} \rho_{51} - i \rho_{101} \Omega{\left(10,5,0 \right)} + \frac{0.0645497224367903 \sqrt{5} \rho_{1010}}{\tau} + \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1111}}{\tau} + \frac{0.186338998124982 \rho_{1115}}{\tau} + \frac{0.372677996249965 \rho_{119}}{\tau} + \frac{0.129099444873581 \sqrt{5} \rho_{1313}}{\tau} - i \rho_{141} \Omega{\left(14,5,0 \right)} + \frac{0.322748612183951 \rho_{1410}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1414}}{\tau} + \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1515}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - i \rho_{201} \Omega{\left(20,5,0 \right)} + i \rho_{510} \Omega{\left(10,1,0 \right)} + i \rho_{514} \Omega{\left(14,1,0 \right)} + \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{52} = \Delta_{52} \rho_{52} - \frac{0.322748612183951 \rho_{1014}}{\tau} - i \rho_{102} \Omega{\left(10,5,0 \right)} + \frac{0.322748612183951 \rho_{1216}}{\tau} - \frac{0.322748612183951 \rho_{1410}}{\tau} - i \rho_{142} \Omega{\left(14,5,0 \right)} - \frac{0.333333333333333 \rho_{159}}{\tau} + \frac{0.322748612183951 \rho_{1612}}{\tau} - i \rho_{202} \Omega{\left(20,5,0 \right)} + i \rho_{515} \Omega{\left(15,2,0 \right)} + i \rho_{59} \Omega{\left(9,2,0 \right)} - \frac{0.333333333333333 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{53} = \Delta_{53} \rho_{53} - i \rho_{103} \Omega{\left(10,5,0 \right)} - \frac{0.186338998124982 \rho_{1115}}{\tau} - \frac{0.372677996249965 \rho_{119}}{\tau} - \frac{0.322748612183951 \rho_{1216}}{\tau} - i \rho_{143} \Omega{\left(14,5,0 \right)} - \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - \frac{0.322748612183951 \rho_{1612}}{\tau} - i \rho_{203} \Omega{\left(20,5,0 \right)} + i \rho_{512} \Omega{\left(12,3,0 \right)} + i \rho_{516} \Omega{\left(16,3,0 \right)} - \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{54} = \frac{0.129099444873581 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - i \rho_{104} \Omega{\left(10,5,0 \right)} + \frac{0.333333333333333 \rho_{1319}}{\tau} + \frac{0.129099444873581 \rho_{1410}}{\tau} + \frac{0.105409255338946 \rho_{1420}}{\tau} - i \rho_{144} \Omega{\left(14,5,0 \right)} + \frac{0.333333333333333 \rho_{1913}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} + \frac{0.105409255338946 \rho_{2014}}{\tau} - i \rho_{204} \Omega{\left(20,5,0 \right)} + i \rho_{513} \Omega{\left(13,4,0 \right)} + i \rho_{519} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{55} = \frac{0.05 \rho_{1010}}{\tau} - \frac{0.0645497224367903 \rho_{1014}}{\tau} - \frac{0.163299316185545 \rho_{1020}}{\tau} - i \rho_{105} \Omega{\left(10,5,0 \right)} + \frac{0.05 \rho_{1111}}{\tau} + \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} + \frac{0.166666666666667 \rho_{1313}}{\tau} - \frac{0.333333333333333 \rho_{1319}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} + \frac{0.0833333333333333 \rho_{1414}}{\tau} + \frac{0.210818510677892 \rho_{1420}}{\tau} - i \rho_{145} \Omega{\left(14,5,0 \right)} + \frac{0.11180339887499 \rho_{1511}}{\tau} + \frac{0.25 \rho_{1515}}{\tau} + \frac{0.223606797749979 \rho_{1521}}{\tau} - \frac{0.333333333333333 \rho_{1913}}{\tau} + \frac{0.666666666666667 \rho_{1919}}{\tau} - \frac{0.163299316185545 \rho_{2010}}{\tau} + \frac{0.210818510677892 \rho_{2014}}{\tau} + \frac{0.533333333333334 \rho_{2020}}{\tau} - i \rho_{205} \Omega{\left(20,5,0 \right)} + \frac{0.1 \rho_{2111}}{\tau} + \frac{0.223606797749979 \rho_{2115}}{\tau} + \frac{0.2 \rho_{2121}}{\tau} + i \rho_{510} \Omega{\left(10,5,0 \right)} + i \rho_{514} \Omega{\left(14,5,0 \right)} + i \rho_{520} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{56} = - \frac{0.0645497224367903 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - i \rho_{106} \Omega{\left(10,5,0 \right)} - \frac{0.2 \rho_{1121}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} + \frac{0.0816496580927726 \rho_{1222}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} - \frac{0.316227766016838 \rho_{1420}}{\tau} - i \rho_{146} \Omega{\left(14,5,0 \right)} + \frac{0.0645497224367903 \rho_{1612}}{\tau} + \frac{0.316227766016838 \rho_{1622}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} - \frac{0.316227766016838 \rho_{2014}}{\tau} - i \rho_{206} \Omega{\left(20,5,0 \right)} - \frac{0.2 \rho_{2111}}{\tau} + \frac{0.0816496580927726 \rho_{2212}}{\tau} + \frac{0.316227766016838 \rho_{2216}}{\tau} + i \rho_{511} \Omega{\left(11,6,0 \right)} + i \rho_{521} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{57} = - i \rho_{107} \Omega{\left(10,5,0 \right)} - \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} - \frac{0.163299316185545 \rho_{1222}}{\tau} - i \rho_{147} \Omega{\left(14,5,0 \right)} - \frac{0.11180339887499 \rho_{1511}}{\tau} - \frac{0.223606797749979 \rho_{1521}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} - \frac{0.210818510677892 \rho_{1622}}{\tau} + \frac{0.333333333333333 \rho_{1723}}{\tau} - i \rho_{207} \Omega{\left(20,5,0 \right)} + \frac{0.1 \rho_{2111}}{\tau} - \frac{0.223606797749979 \rho_{2115}}{\tau} - \frac{0.163299316185545 \rho_{2212}}{\tau} - \frac{0.210818510677892 \rho_{2216}}{\tau} + \frac{0.333333333333333 \rho_{2317}}{\tau} + i \rho_{512} \Omega{\left(12,7,0 \right)} + i \rho_{516} \Omega{\left(16,7,0 \right)} + i \rho_{522} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{58} = - i \rho_{108} \Omega{\left(10,5,0 \right)} - \frac{0.129099444873581 \rho_{1216}}{\tau} + \frac{0.0816496580927727 \rho_{1222}}{\tau} - i \rho_{148} \Omega{\left(14,5,0 \right)} - \frac{0.129099444873581 \rho_{1612}}{\tau} - \frac{0.105409255338946 \rho_{1622}}{\tau} - \frac{0.333333333333333 \rho_{1723}}{\tau} - i \rho_{208} \Omega{\left(20,5,0 \right)} + \frac{0.0816496580927727 \rho_{2212}}{\tau} - \frac{0.105409255338946 \rho_{2216}}{\tau} - \frac{0.333333333333333 \rho_{2317}}{\tau} + i \rho_{517} \Omega{\left(17,8,0 \right)} + i \rho_{523} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{61} = \Delta_{61} \rho_{61} + \frac{0.322748612183951 \rho_{1014}}{\tau} - i \rho_{111} \Omega{\left(11,6,0 \right)} + \frac{0.186338998124982 \rho_{1115}}{\tau} + \frac{0.372677996249965 \rho_{119}}{\tau} + \frac{0.322748612183951 \rho_{1410}}{\tau} + \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - i \rho_{211} \Omega{\left(21,6,0 \right)} + i \rho_{610} \Omega{\left(10,1,0 \right)} + i \rho_{614} \Omega{\left(14,1,0 \right)} + \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{62} = \Delta_{62} \rho_{62} + \frac{0.0215165741455968 \sqrt{15} \rho_{1010}}{\tau} - \frac{0.322748612183951 \rho_{1014}}{\tau} - i \rho_{112} \Omega{\left(11,6,0 \right)} + \frac{0.0215165741455968 \sqrt{15} \rho_{1212}}{\tau} + \frac{0.322748612183951 \rho_{1216}}{\tau} - \frac{0.322748612183951 \rho_{1410}}{\tau} + \frac{0.0645497224367903 \sqrt{15} \rho_{1414}}{\tau} - \frac{0.333333333333333 \rho_{159}}{\tau} + \frac{0.322748612183951 \rho_{1612}}{\tau} + \frac{0.0645497224367903 \sqrt{15} \rho_{1616}}{\tau} - i \rho_{212} \Omega{\left(21,6,0 \right)} + i \rho_{615} \Omega{\left(15,2,0 \right)} + i \rho_{69} \Omega{\left(9,2,0 \right)} - \frac{0.333333333333333 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{63} = \Delta_{63} \rho_{63} - \frac{0.186338998124982 \rho_{1115}}{\tau} - i \rho_{113} \Omega{\left(11,6,0 \right)} - \frac{0.372677996249965 \rho_{119}}{\tau} - \frac{0.322748612183951 \rho_{1216}}{\tau} - \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - \frac{0.322748612183951 \rho_{1612}}{\tau} - i \rho_{213} \Omega{\left(21,6,0 \right)} + i \rho_{612} \Omega{\left(12,3,0 \right)} + i \rho_{616} \Omega{\left(16,3,0 \right)} - \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{64} = \frac{0.129099444873581 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - i \rho_{114} \Omega{\left(11,6,0 \right)} + \frac{0.333333333333333 \rho_{1319}}{\tau} + \frac{0.129099444873581 \rho_{1410}}{\tau} + \frac{0.105409255338946 \rho_{1420}}{\tau} + \frac{0.333333333333333 \rho_{1913}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} + \frac{0.105409255338946 \rho_{2014}}{\tau} - i \rho_{214} \Omega{\left(21,6,0 \right)} + i \rho_{613} \Omega{\left(13,4,0 \right)} + i \rho_{619} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{65} = - \frac{0.0645497224367903 \rho_{1014}}{\tau} - \frac{0.163299316185545 \rho_{1020}}{\tau} + \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} - i \rho_{115} \Omega{\left(11,6,0 \right)} - \frac{0.333333333333333 \rho_{1319}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} + \frac{0.210818510677892 \rho_{1420}}{\tau} + \frac{0.11180339887499 \rho_{1511}}{\tau} + \frac{0.223606797749979 \rho_{1521}}{\tau} - \frac{0.333333333333333 \rho_{1913}}{\tau} - \frac{0.163299316185545 \rho_{2010}}{\tau} + \frac{0.210818510677892 \rho_{2014}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} + \frac{0.223606797749979 \rho_{2115}}{\tau} - i \rho_{215} \Omega{\left(21,6,0 \right)} + i \rho_{610} \Omega{\left(10,5,0 \right)} + i \rho_{614} \Omega{\left(14,5,0 \right)} + i \rho_{620} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{66} = \frac{0.0166666666666667 \rho_{1010}}{\tau} - \frac{0.0645497224367903 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} + \frac{0.0666666666666667 \rho_{1111}}{\tau} - \frac{0.2 \rho_{1121}}{\tau} - i \rho_{116} \Omega{\left(11,6,0 \right)} + \frac{0.0166666666666667 \rho_{1212}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} + \frac{0.0816496580927726 \rho_{1222}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} + \frac{0.25 \rho_{1414}}{\tau} - \frac{0.316227766016838 \rho_{1420}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} + \frac{0.25 \rho_{1616}}{\tau} + \frac{0.316227766016838 \rho_{1622}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} - \frac{0.316227766016838 \rho_{2014}}{\tau} + \frac{0.4 \rho_{2020}}{\tau} - \frac{0.2 \rho_{2111}}{\tau} + \frac{0.6 \rho_{2121}}{\tau} - i \rho_{216} \Omega{\left(21,6,0 \right)} + \frac{0.0816496580927726 \rho_{2212}}{\tau} + \frac{0.316227766016838 \rho_{2216}}{\tau} + \frac{0.4 \rho_{2222}}{\tau} + i \rho_{611} \Omega{\left(11,6,0 \right)} + i \rho_{621} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{67} = - \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} - i \rho_{117} \Omega{\left(11,6,0 \right)} + \frac{0.0645497224367903 \rho_{1216}}{\tau} - \frac{0.163299316185545 \rho_{1222}}{\tau} - \frac{0.11180339887499 \rho_{1511}}{\tau} - \frac{0.223606797749979 \rho_{1521}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} - \frac{0.210818510677892 \rho_{1622}}{\tau} + \frac{0.333333333333333 \rho_{1723}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} - \frac{0.223606797749979 \rho_{2115}}{\tau} - i \rho_{217} \Omega{\left(21,6,0 \right)} - \frac{0.163299316185545 \rho_{2212}}{\tau} - \frac{0.210818510677892 \rho_{2216}}{\tau} + \frac{0.333333333333333 \rho_{2317}}{\tau} + i \rho_{612} \Omega{\left(12,7,0 \right)} + i \rho_{616} \Omega{\left(16,7,0 \right)} + i \rho_{622} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{68} = - i \rho_{118} \Omega{\left(11,6,0 \right)} - \frac{0.129099444873581 \rho_{1216}}{\tau} + \frac{0.0816496580927727 \rho_{1222}}{\tau} - \frac{0.129099444873581 \rho_{1612}}{\tau} - \frac{0.105409255338946 \rho_{1622}}{\tau} - \frac{0.333333333333333 \rho_{1723}}{\tau} - i \rho_{218} \Omega{\left(21,6,0 \right)} + \frac{0.0816496580927727 \rho_{2212}}{\tau} - \frac{0.105409255338946 \rho_{2216}}{\tau} - \frac{0.333333333333333 \rho_{2317}}{\tau} + i \rho_{617} \Omega{\left(17,8,0 \right)} + i \rho_{623} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{71} = \Delta_{71} \rho_{71} + \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.186338998124982 \rho_{1115}}{\tau} + \frac{0.372677996249965 \rho_{119}}{\tau} - i \rho_{121} \Omega{\left(12,7,0 \right)} + \frac{0.322748612183951 \rho_{1410}}{\tau} + \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - i \rho_{161} \Omega{\left(16,7,0 \right)} - i \rho_{221} \Omega{\left(22,7,0 \right)} + i \rho_{710} \Omega{\left(10,1,0 \right)} + i \rho_{714} \Omega{\left(14,1,0 \right)} + \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{72} = \Delta_{72} \rho_{72} - \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.322748612183951 \rho_{1216}}{\tau} - i \rho_{122} \Omega{\left(12,7,0 \right)} - \frac{0.322748612183951 \rho_{1410}}{\tau} - \frac{0.333333333333333 \rho_{159}}{\tau} + \frac{0.322748612183951 \rho_{1612}}{\tau} - i \rho_{162} \Omega{\left(16,7,0 \right)} - i \rho_{222} \Omega{\left(22,7,0 \right)} + i \rho_{715} \Omega{\left(15,2,0 \right)} + i \rho_{79} \Omega{\left(9,2,0 \right)} - \frac{0.333333333333333 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{73} = \Delta_{73} \rho_{73} + \frac{0.0645497224367903 \sqrt{5} \rho_{1111}}{\tau} - \frac{0.186338998124982 \rho_{1115}}{\tau} - \frac{0.372677996249965 \rho_{119}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1212}}{\tau} - \frac{0.322748612183951 \rho_{1216}}{\tau} - i \rho_{123} \Omega{\left(12,7,0 \right)} - \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1515}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - \frac{0.322748612183951 \rho_{1612}}{\tau} + \frac{0.0645497224367903 \sqrt{5} \rho_{1616}}{\tau} - i \rho_{163} \Omega{\left(16,7,0 \right)} + \frac{0.129099444873581 \sqrt{5} \rho_{1717}}{\tau} - i \rho_{223} \Omega{\left(22,7,0 \right)} + i \rho_{712} \Omega{\left(12,3,0 \right)} + i \rho_{716} \Omega{\left(16,3,0 \right)} - \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{74} = \frac{0.129099444873581 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - i \rho_{124} \Omega{\left(12,7,0 \right)} + \frac{0.333333333333333 \rho_{1319}}{\tau} + \frac{0.129099444873581 \rho_{1410}}{\tau} + \frac{0.105409255338946 \rho_{1420}}{\tau} - i \rho_{164} \Omega{\left(16,7,0 \right)} + \frac{0.333333333333333 \rho_{1913}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} + \frac{0.105409255338946 \rho_{2014}}{\tau} - i \rho_{224} \Omega{\left(22,7,0 \right)} + i \rho_{713} \Omega{\left(13,4,0 \right)} + i \rho_{719} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{75} = - \frac{0.0645497224367903 \rho_{1014}}{\tau} - \frac{0.163299316185545 \rho_{1020}}{\tau} + \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} - i \rho_{125} \Omega{\left(12,7,0 \right)} - \frac{0.333333333333333 \rho_{1319}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} + \frac{0.210818510677892 \rho_{1420}}{\tau} + \frac{0.11180339887499 \rho_{1511}}{\tau} + \frac{0.223606797749979 \rho_{1521}}{\tau} - i \rho_{165} \Omega{\left(16,7,0 \right)} - \frac{0.333333333333333 \rho_{1913}}{\tau} - \frac{0.163299316185545 \rho_{2010}}{\tau} + \frac{0.210818510677892 \rho_{2014}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} + \frac{0.223606797749979 \rho_{2115}}{\tau} - i \rho_{225} \Omega{\left(22,7,0 \right)} + i \rho_{710} \Omega{\left(10,5,0 \right)} + i \rho_{714} \Omega{\left(14,5,0 \right)} + i \rho_{720} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{76} = - \frac{0.0645497224367903 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - \frac{0.2 \rho_{1121}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} + \frac{0.0816496580927726 \rho_{1222}}{\tau} - i \rho_{126} \Omega{\left(12,7,0 \right)} - \frac{0.0645497224367903 \rho_{1410}}{\tau} - \frac{0.316227766016838 \rho_{1420}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} + \frac{0.316227766016838 \rho_{1622}}{\tau} - i \rho_{166} \Omega{\left(16,7,0 \right)} + \frac{0.0816496580927726 \rho_{2010}}{\tau} - \frac{0.316227766016838 \rho_{2014}}{\tau} - \frac{0.2 \rho_{2111}}{\tau} + \frac{0.0816496580927726 \rho_{2212}}{\tau} + \frac{0.316227766016838 \rho_{2216}}{\tau} - i \rho_{226} \Omega{\left(22,7,0 \right)} + i \rho_{711} \Omega{\left(11,6,0 \right)} + i \rho_{721} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{77} = \frac{0.05 \rho_{1111}}{\tau} - \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} + \frac{0.05 \rho_{1212}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} - \frac{0.163299316185545 \rho_{1222}}{\tau} - i \rho_{127} \Omega{\left(12,7,0 \right)} - \frac{0.11180339887499 \rho_{1511}}{\tau} + \frac{0.25 \rho_{1515}}{\tau} - \frac{0.223606797749979 \rho_{1521}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} + \frac{0.0833333333333333 \rho_{1616}}{\tau} - \frac{0.210818510677892 \rho_{1622}}{\tau} - i \rho_{167} \Omega{\left(16,7,0 \right)} + \frac{0.166666666666667 \rho_{1717}}{\tau} + \frac{0.333333333333333 \rho_{1723}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} - \frac{0.223606797749979 \rho_{2115}}{\tau} + \frac{0.2 \rho_{2121}}{\tau} - \frac{0.163299316185545 \rho_{2212}}{\tau} - \frac{0.210818510677892 \rho_{2216}}{\tau} + \frac{0.533333333333334 \rho_{2222}}{\tau} - i \rho_{227} \Omega{\left(22,7,0 \right)} + \frac{0.333333333333333 \rho_{2317}}{\tau} + \frac{0.666666666666667 \rho_{2323}}{\tau} + i \rho_{712} \Omega{\left(12,7,0 \right)} + i \rho_{716} \Omega{\left(16,7,0 \right)} + i \rho_{722} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{78} = - \frac{0.129099444873581 \rho_{1216}}{\tau} + \frac{0.0816496580927727 \rho_{1222}}{\tau} - i \rho_{128} \Omega{\left(12,7,0 \right)} - \frac{0.129099444873581 \rho_{1612}}{\tau} - \frac{0.105409255338946 \rho_{1622}}{\tau} - i \rho_{168} \Omega{\left(16,7,0 \right)} - \frac{0.333333333333333 \rho_{1723}}{\tau} + \frac{0.0816496580927727 \rho_{2212}}{\tau} - \frac{0.105409255338946 \rho_{2216}}{\tau} - i \rho_{228} \Omega{\left(22,7,0 \right)} - \frac{0.333333333333333 \rho_{2317}}{\tau} + i \rho_{717} \Omega{\left(17,8,0 \right)} + i \rho_{723} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{81} = \Delta_{81} \rho_{81} + \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.186338998124982 \rho_{1115}}{\tau} + \frac{0.372677996249965 \rho_{119}}{\tau} + \frac{0.322748612183951 \rho_{1410}}{\tau} + \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - i \rho_{171} \Omega{\left(17,8,0 \right)} - i \rho_{231} \Omega{\left(23,8,0 \right)} + i \rho_{810} \Omega{\left(10,1,0 \right)} + i \rho_{814} \Omega{\left(14,1,0 \right)} + \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{82} = \Delta_{82} \rho_{82} - \frac{0.322748612183951 \rho_{1014}}{\tau} + \frac{0.322748612183951 \rho_{1216}}{\tau} - \frac{0.322748612183951 \rho_{1410}}{\tau} - \frac{0.333333333333333 \rho_{159}}{\tau} + \frac{0.322748612183951 \rho_{1612}}{\tau} - i \rho_{172} \Omega{\left(17,8,0 \right)} - i \rho_{232} \Omega{\left(23,8,0 \right)} + i \rho_{815} \Omega{\left(15,2,0 \right)} + i \rho_{89} \Omega{\left(9,2,0 \right)} - \frac{0.333333333333333 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{83} = \Delta_{83} \rho_{83} - \frac{0.186338998124982 \rho_{1115}}{\tau} - \frac{0.372677996249965 \rho_{119}}{\tau} - \frac{0.322748612183951 \rho_{1216}}{\tau} - \frac{0.186338998124982 \rho_{1511}}{\tau} + \frac{0.166666666666667 \rho_{159}}{\tau} - \frac{0.322748612183951 \rho_{1612}}{\tau} - i \rho_{173} \Omega{\left(17,8,0 \right)} - i \rho_{233} \Omega{\left(23,8,0 \right)} + i \rho_{812} \Omega{\left(12,3,0 \right)} + i \rho_{816} \Omega{\left(16,3,0 \right)} - \frac{0.372677996249965 \rho_{911}}{\tau} + \frac{0.166666666666667 \rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{84} = \frac{0.129099444873581 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} + \frac{0.333333333333333 \rho_{1319}}{\tau} + \frac{0.129099444873581 \rho_{1410}}{\tau} + \frac{0.105409255338946 \rho_{1420}}{\tau} - i \rho_{174} \Omega{\left(17,8,0 \right)} + \frac{0.333333333333333 \rho_{1913}}{\tau} + \frac{0.0816496580927726 \rho_{2010}}{\tau} + \frac{0.105409255338946 \rho_{2014}}{\tau} - i \rho_{234} \Omega{\left(23,8,0 \right)} + i \rho_{813} \Omega{\left(13,4,0 \right)} + i \rho_{819} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{85} = - \frac{0.0645497224367903 \rho_{1014}}{\tau} - \frac{0.163299316185545 \rho_{1020}}{\tau} + \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} - \frac{0.333333333333333 \rho_{1319}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} + \frac{0.210818510677892 \rho_{1420}}{\tau} + \frac{0.11180339887499 \rho_{1511}}{\tau} + \frac{0.223606797749979 \rho_{1521}}{\tau} - i \rho_{175} \Omega{\left(17,8,0 \right)} - \frac{0.333333333333333 \rho_{1913}}{\tau} - \frac{0.163299316185545 \rho_{2010}}{\tau} + \frac{0.210818510677892 \rho_{2014}}{\tau} + \frac{0.1 \rho_{2111}}{\tau} + \frac{0.223606797749979 \rho_{2115}}{\tau} - i \rho_{235} \Omega{\left(23,8,0 \right)} + i \rho_{810} \Omega{\left(10,5,0 \right)} + i \rho_{814} \Omega{\left(14,5,0 \right)} + i \rho_{820} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{86} = - \frac{0.0645497224367903 \rho_{1014}}{\tau} + \frac{0.0816496580927726 \rho_{1020}}{\tau} - \frac{0.2 \rho_{1121}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} + \frac{0.0816496580927726 \rho_{1222}}{\tau} - \frac{0.0645497224367903 \rho_{1410}}{\tau} - \frac{0.316227766016838 \rho_{1420}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} + \frac{0.316227766016838 \rho_{1622}}{\tau} - i \rho_{176} \Omega{\left(17,8,0 \right)} + \frac{0.0816496580927726 \rho_{2010}}{\tau} - \frac{0.316227766016838 \rho_{2014}}{\tau} - \frac{0.2 \rho_{2111}}{\tau} + \frac{0.0816496580927726 \rho_{2212}}{\tau} + \frac{0.316227766016838 \rho_{2216}}{\tau} - i \rho_{236} \Omega{\left(23,8,0 \right)} + i \rho_{811} \Omega{\left(11,6,0 \right)} + i \rho_{821} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{87} = - \frac{0.11180339887499 \rho_{1115}}{\tau} + \frac{0.1 \rho_{1121}}{\tau} + \frac{0.0645497224367903 \rho_{1216}}{\tau} - \frac{0.163299316185545 \rho_{1222}}{\tau} - \frac{0.11180339887499 \rho_{1511}}{\tau} - \frac{0.223606797749979 \rho_{1521}}{\tau} + \frac{0.0645497224367903 \rho_{1612}}{\tau} - \frac{0.210818510677892 \rho_{1622}}{\tau} + \frac{0.333333333333333 \rho_{1723}}{\tau} - i \rho_{177} \Omega{\left(17,8,0 \right)} + \frac{0.1 \rho_{2111}}{\tau} - \frac{0.223606797749979 \rho_{2115}}{\tau} - \frac{0.163299316185545 \rho_{2212}}{\tau} - \frac{0.210818510677892 \rho_{2216}}{\tau} + \frac{0.333333333333333 \rho_{2317}}{\tau} - i \rho_{237} \Omega{\left(23,8,0 \right)} + i \rho_{812} \Omega{\left(12,7,0 \right)} + i \rho_{816} \Omega{\left(16,7,0 \right)} + i \rho_{822} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{88} = \frac{0.1 \rho_{1212}}{\tau} - \frac{0.129099444873581 \rho_{1216}}{\tau} + \frac{0.0816496580927727 \rho_{1222}}{\tau} - \frac{0.129099444873581 \rho_{1612}}{\tau} + \frac{0.166666666666667 \rho_{1616}}{\tau} - \frac{0.105409255338946 \rho_{1622}}{\tau} + \frac{0.333333333333333 \rho_{1717}}{\tau} - \frac{0.333333333333333 \rho_{1723}}{\tau} - i \rho_{178} \Omega{\left(17,8,0 \right)} + \frac{0.0816496580927727 \rho_{2212}}{\tau} - \frac{0.105409255338946 \rho_{2216}}{\tau} + \frac{0.0666666666666667 \rho_{2222}}{\tau} - \frac{0.333333333333333 \rho_{2317}}{\tau} + \frac{0.333333333333333 \rho_{2323}}{\tau} - i \rho_{238} \Omega{\left(23,8,0 \right)} + \frac{1.0 \rho_{2424}}{\tau} + i \rho_{817} \Omega{\left(17,8,0 \right)} + i \rho_{823} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{99} = - i \rho_{29} \Omega{\left(9,2,0 \right)} + i \rho_{99} \Omega{\left(9,2,0 \right)} - \frac{\rho_{99}}{\tau}$

$\displaystyle \dot{\rho}_{910} = \Delta_{910} \rho_{910} - i \rho_{210} \Omega{\left(9,2,0 \right)} + i \rho_{910} \Omega{\left(10,1,0 \right)} + i \rho_{910} \Omega{\left(10,5,0 \right)} - \frac{\rho_{910}}{\tau}$

$\displaystyle \dot{\rho}_{911} = \Delta_{911} \rho_{911} - i \rho_{211} \Omega{\left(9,2,0 \right)} + i \rho_{911} \Omega{\left(11,6,0 \right)} - \frac{\rho_{911}}{\tau}$

$\displaystyle \dot{\rho}_{912} = \Delta_{912} \rho_{912} - i \rho_{212} \Omega{\left(9,2,0 \right)} + i \rho_{912} \Omega{\left(12,3,0 \right)} + i \rho_{912} \Omega{\left(12,7,0 \right)} - \frac{\rho_{912}}{\tau}$

$\displaystyle \dot{\rho}_{913} = \Delta_{913} \rho_{913} - i \rho_{213} \Omega{\left(9,2,0 \right)} + i \rho_{913} \Omega{\left(13,4,0 \right)} - \frac{\rho_{913}}{\tau}$

$\displaystyle \dot{\rho}_{914} = \Delta_{914} \rho_{914} - i \rho_{214} \Omega{\left(9,2,0 \right)} + i \rho_{914} \Omega{\left(14,1,0 \right)} + i \rho_{914} \Omega{\left(14,5,0 \right)} - \frac{\rho_{914}}{\tau}$

$\displaystyle \dot{\rho}_{915} = \Delta_{915} \rho_{915} - i \rho_{215} \Omega{\left(9,2,0 \right)} + i \rho_{915} \Omega{\left(15,2,0 \right)} - \frac{\rho_{915}}{\tau}$

$\displaystyle \dot{\rho}_{916} = \Delta_{916} \rho_{916} - i \rho_{216} \Omega{\left(9,2,0 \right)} + i \rho_{916} \Omega{\left(16,3,0 \right)} + i \rho_{916} \Omega{\left(16,7,0 \right)} - \frac{\rho_{916}}{\tau}$

$\displaystyle \dot{\rho}_{917} = \Delta_{917} \rho_{917} - i \rho_{217} \Omega{\left(9,2,0 \right)} + i \rho_{917} \Omega{\left(17,8,0 \right)} - \frac{\rho_{917}}{\tau}$

$\displaystyle \dot{\rho}_{918} = \Delta_{918} \rho_{918} - i \rho_{218} \Omega{\left(9,2,0 \right)} - \frac{\rho_{918}}{\tau}$

$\displaystyle \dot{\rho}_{919} = \Delta_{919} \rho_{919} - i \rho_{219} \Omega{\left(9,2,0 \right)} + i \rho_{919} \Omega{\left(19,4,0 \right)} - \frac{\rho_{919}}{\tau}$

$\displaystyle \dot{\rho}_{920} = \Delta_{920} \rho_{920} - i \rho_{220} \Omega{\left(9,2,0 \right)} + i \rho_{920} \Omega{\left(20,5,0 \right)} - \frac{\rho_{920}}{\tau}$

$\displaystyle \dot{\rho}_{921} = \Delta_{921} \rho_{921} - i \rho_{221} \Omega{\left(9,2,0 \right)} + i \rho_{921} \Omega{\left(21,6,0 \right)} - \frac{\rho_{921}}{\tau}$

$\displaystyle \dot{\rho}_{922} = \Delta_{922} \rho_{922} - i \rho_{222} \Omega{\left(9,2,0 \right)} + i \rho_{922} \Omega{\left(22,7,0 \right)} - \frac{\rho_{922}}{\tau}$

$\displaystyle \dot{\rho}_{923} = \Delta_{923} \rho_{923} - i \rho_{223} \Omega{\left(9,2,0 \right)} + i \rho_{923} \Omega{\left(23,8,0 \right)} - \frac{\rho_{923}}{\tau}$

$\displaystyle \dot{\rho}_{924} = \Delta_{924} \rho_{924} - i \rho_{224} \Omega{\left(9,2,0 \right)} - \frac{\rho_{924}}{\tau}$

$\displaystyle \dot{\rho}_{109} = \Delta_{109} \rho_{109} + i \rho_{109} \Omega{\left(9,2,0 \right)} - \frac{\rho_{109}}{\tau} - i \rho_{19} \Omega{\left(10,1,0 \right)} - i \rho_{59} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1010} = i \rho_{1010} \Omega{\left(10,1,0 \right)} + i \rho_{1010} \Omega{\left(10,5,0 \right)} - \frac{\rho_{1010}}{\tau} - i \rho_{110} \Omega{\left(10,1,0 \right)} - i \rho_{510} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1011} = i \rho_{1011} \Omega{\left(11,6,0 \right)} - \frac{\rho_{1011}}{\tau} - i \rho_{111} \Omega{\left(10,1,0 \right)} - i \rho_{511} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1012} = i \rho_{1012} \Omega{\left(12,3,0 \right)} + i \rho_{1012} \Omega{\left(12,7,0 \right)} - \frac{\rho_{1012}}{\tau} - i \rho_{112} \Omega{\left(10,1,0 \right)} - i \rho_{512} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1013} = \Delta_{1013} \rho_{1013} + i \rho_{1013} \Omega{\left(13,4,0 \right)} - \frac{\rho_{1013}}{\tau} - i \rho_{113} \Omega{\left(10,1,0 \right)} - i \rho_{513} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1014} = \Delta_{1014} \rho_{1014} + i \rho_{1014} \Omega{\left(14,1,0 \right)} + i \rho_{1014} \Omega{\left(14,5,0 \right)} - \frac{\rho_{1014}}{\tau} - i \rho_{114} \Omega{\left(10,1,0 \right)} - i \rho_{514} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1015} = \Delta_{1015} \rho_{1015} + i \rho_{1015} \Omega{\left(15,2,0 \right)} - \frac{\rho_{1015}}{\tau} - i \rho_{115} \Omega{\left(10,1,0 \right)} - i \rho_{515} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1016} = \Delta_{1016} \rho_{1016} + i \rho_{1016} \Omega{\left(16,3,0 \right)} + i \rho_{1016} \Omega{\left(16,7,0 \right)} - \frac{\rho_{1016}}{\tau} - i \rho_{116} \Omega{\left(10,1,0 \right)} - i \rho_{516} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1017} = \Delta_{1017} \rho_{1017} + i \rho_{1017} \Omega{\left(17,8,0 \right)} - \frac{\rho_{1017}}{\tau} - i \rho_{117} \Omega{\left(10,1,0 \right)} - i \rho_{517} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1018} = \Delta_{1018} \rho_{1018} - \frac{\rho_{1018}}{\tau} - i \rho_{118} \Omega{\left(10,1,0 \right)} - i \rho_{518} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1019} = \Delta_{1019} \rho_{1019} + i \rho_{1019} \Omega{\left(19,4,0 \right)} - \frac{\rho_{1019}}{\tau} - i \rho_{119} \Omega{\left(10,1,0 \right)} - i \rho_{519} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1020} = \Delta_{1020} \rho_{1020} + i \rho_{1020} \Omega{\left(20,5,0 \right)} - \frac{\rho_{1020}}{\tau} - i \rho_{120} \Omega{\left(10,1,0 \right)} - i \rho_{520} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1021} = \Delta_{1021} \rho_{1021} + i \rho_{1021} \Omega{\left(21,6,0 \right)} - \frac{\rho_{1021}}{\tau} - i \rho_{121} \Omega{\left(10,1,0 \right)} - i \rho_{521} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1022} = \Delta_{1022} \rho_{1022} + i \rho_{1022} \Omega{\left(22,7,0 \right)} - \frac{\rho_{1022}}{\tau} - i \rho_{122} \Omega{\left(10,1,0 \right)} - i \rho_{522} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1023} = \Delta_{1023} \rho_{1023} + i \rho_{1023} \Omega{\left(23,8,0 \right)} - \frac{\rho_{1023}}{\tau} - i \rho_{123} \Omega{\left(10,1,0 \right)} - i \rho_{523} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{1024} = \Delta_{1024} \rho_{1024} - \frac{\rho_{1024}}{\tau} - i \rho_{124} \Omega{\left(10,1,0 \right)} - i \rho_{524} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{119} = \Delta_{119} \rho_{119} + i \rho_{119} \Omega{\left(9,2,0 \right)} - \frac{\rho_{119}}{\tau} - i \rho_{69} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1110} = i \rho_{1110} \Omega{\left(10,1,0 \right)} + i \rho_{1110} \Omega{\left(10,5,0 \right)} - \frac{\rho_{1110}}{\tau} - i \rho_{610} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1111} = i \rho_{1111} \Omega{\left(11,6,0 \right)} - \frac{\rho_{1111}}{\tau} - i \rho_{611} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1112} = i \rho_{1112} \Omega{\left(12,3,0 \right)} + i \rho_{1112} \Omega{\left(12,7,0 \right)} - \frac{\rho_{1112}}{\tau} - i \rho_{612} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1113} = \Delta_{1113} \rho_{1113} + i \rho_{1113} \Omega{\left(13,4,0 \right)} - \frac{\rho_{1113}}{\tau} - i \rho_{613} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1114} = \Delta_{1114} \rho_{1114} + i \rho_{1114} \Omega{\left(14,1,0 \right)} + i \rho_{1114} \Omega{\left(14,5,0 \right)} - \frac{\rho_{1114}}{\tau} - i \rho_{614} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1115} = \Delta_{1115} \rho_{1115} + i \rho_{1115} \Omega{\left(15,2,0 \right)} - \frac{\rho_{1115}}{\tau} - i \rho_{615} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1116} = \Delta_{1116} \rho_{1116} + i \rho_{1116} \Omega{\left(16,3,0 \right)} + i \rho_{1116} \Omega{\left(16,7,0 \right)} - \frac{\rho_{1116}}{\tau} - i \rho_{616} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1117} = \Delta_{1117} \rho_{1117} + i \rho_{1117} \Omega{\left(17,8,0 \right)} - \frac{\rho_{1117}}{\tau} - i \rho_{617} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1118} = \Delta_{1118} \rho_{1118} - \frac{\rho_{1118}}{\tau} - i \rho_{618} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1119} = \Delta_{1119} \rho_{1119} + i \rho_{1119} \Omega{\left(19,4,0 \right)} - \frac{\rho_{1119}}{\tau} - i \rho_{619} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1120} = \Delta_{1120} \rho_{1120} + i \rho_{1120} \Omega{\left(20,5,0 \right)} - \frac{\rho_{1120}}{\tau} - i \rho_{620} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1121} = \Delta_{1121} \rho_{1121} + i \rho_{1121} \Omega{\left(21,6,0 \right)} - \frac{\rho_{1121}}{\tau} - i \rho_{621} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1122} = \Delta_{1122} \rho_{1122} + i \rho_{1122} \Omega{\left(22,7,0 \right)} - \frac{\rho_{1122}}{\tau} - i \rho_{622} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1123} = \Delta_{1123} \rho_{1123} + i \rho_{1123} \Omega{\left(23,8,0 \right)} - \frac{\rho_{1123}}{\tau} - i \rho_{623} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{1124} = \Delta_{1124} \rho_{1124} - \frac{\rho_{1124}}{\tau} - i \rho_{624} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{129} = \Delta_{129} \rho_{129} + i \rho_{129} \Omega{\left(9,2,0 \right)} - \frac{\rho_{129}}{\tau} - i \rho_{39} \Omega{\left(12,3,0 \right)} - i \rho_{79} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1210} = i \rho_{1210} \Omega{\left(10,1,0 \right)} + i \rho_{1210} \Omega{\left(10,5,0 \right)} - \frac{\rho_{1210}}{\tau} - i \rho_{310} \Omega{\left(12,3,0 \right)} - i \rho_{710} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1211} = i \rho_{1211} \Omega{\left(11,6,0 \right)} - \frac{\rho_{1211}}{\tau} - i \rho_{311} \Omega{\left(12,3,0 \right)} - i \rho_{711} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1212} = i \rho_{1212} \Omega{\left(12,3,0 \right)} + i \rho_{1212} \Omega{\left(12,7,0 \right)} - \frac{\rho_{1212}}{\tau} - i \rho_{312} \Omega{\left(12,3,0 \right)} - i \rho_{712} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1213} = \Delta_{1213} \rho_{1213} + i \rho_{1213} \Omega{\left(13,4,0 \right)} - \frac{\rho_{1213}}{\tau} - i \rho_{313} \Omega{\left(12,3,0 \right)} - i \rho_{713} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1214} = \Delta_{1214} \rho_{1214} + i \rho_{1214} \Omega{\left(14,1,0 \right)} + i \rho_{1214} \Omega{\left(14,5,0 \right)} - \frac{\rho_{1214}}{\tau} - i \rho_{314} \Omega{\left(12,3,0 \right)} - i \rho_{714} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1215} = \Delta_{1215} \rho_{1215} + i \rho_{1215} \Omega{\left(15,2,0 \right)} - \frac{\rho_{1215}}{\tau} - i \rho_{315} \Omega{\left(12,3,0 \right)} - i \rho_{715} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1216} = \Delta_{1216} \rho_{1216} + i \rho_{1216} \Omega{\left(16,3,0 \right)} + i \rho_{1216} \Omega{\left(16,7,0 \right)} - \frac{\rho_{1216}}{\tau} - i \rho_{316} \Omega{\left(12,3,0 \right)} - i \rho_{716} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1217} = \Delta_{1217} \rho_{1217} + i \rho_{1217} \Omega{\left(17,8,0 \right)} - \frac{\rho_{1217}}{\tau} - i \rho_{317} \Omega{\left(12,3,0 \right)} - i \rho_{717} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1218} = \Delta_{1218} \rho_{1218} - \frac{\rho_{1218}}{\tau} - i \rho_{318} \Omega{\left(12,3,0 \right)} - i \rho_{718} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1219} = \Delta_{1219} \rho_{1219} + i \rho_{1219} \Omega{\left(19,4,0 \right)} - \frac{\rho_{1219}}{\tau} - i \rho_{319} \Omega{\left(12,3,0 \right)} - i \rho_{719} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1220} = \Delta_{1220} \rho_{1220} + i \rho_{1220} \Omega{\left(20,5,0 \right)} - \frac{\rho_{1220}}{\tau} - i \rho_{320} \Omega{\left(12,3,0 \right)} - i \rho_{720} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1221} = \Delta_{1221} \rho_{1221} + i \rho_{1221} \Omega{\left(21,6,0 \right)} - \frac{\rho_{1221}}{\tau} - i \rho_{321} \Omega{\left(12,3,0 \right)} - i \rho_{721} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1222} = \Delta_{1222} \rho_{1222} + i \rho_{1222} \Omega{\left(22,7,0 \right)} - \frac{\rho_{1222}}{\tau} - i \rho_{322} \Omega{\left(12,3,0 \right)} - i \rho_{722} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1223} = \Delta_{1223} \rho_{1223} + i \rho_{1223} \Omega{\left(23,8,0 \right)} - \frac{\rho_{1223}}{\tau} - i \rho_{323} \Omega{\left(12,3,0 \right)} - i \rho_{723} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{1224} = \Delta_{1224} \rho_{1224} - \frac{\rho_{1224}}{\tau} - i \rho_{324} \Omega{\left(12,3,0 \right)} - i \rho_{724} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{139} = \Delta_{139} \rho_{139} + i \rho_{139} \Omega{\left(9,2,0 \right)} - \frac{\rho_{139}}{\tau} - i \rho_{49} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1310} = \Delta_{1310} \rho_{1310} + i \rho_{1310} \Omega{\left(10,1,0 \right)} + i \rho_{1310} \Omega{\left(10,5,0 \right)} - \frac{\rho_{1310}}{\tau} - i \rho_{410} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1311} = \Delta_{1311} \rho_{1311} + i \rho_{1311} \Omega{\left(11,6,0 \right)} - \frac{\rho_{1311}}{\tau} - i \rho_{411} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1312} = \Delta_{1312} \rho_{1312} + i \rho_{1312} \Omega{\left(12,3,0 \right)} + i \rho_{1312} \Omega{\left(12,7,0 \right)} - \frac{\rho_{1312}}{\tau} - i \rho_{412} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1313} = i \rho_{1313} \Omega{\left(13,4,0 \right)} - \frac{\rho_{1313}}{\tau} - i \rho_{413} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1314} = i \rho_{1314} \Omega{\left(14,1,0 \right)} + i \rho_{1314} \Omega{\left(14,5,0 \right)} - \frac{\rho_{1314}}{\tau} - i \rho_{414} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1315} = i \rho_{1315} \Omega{\left(15,2,0 \right)} - \frac{\rho_{1315}}{\tau} - i \rho_{415} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1316} = i \rho_{1316} \Omega{\left(16,3,0 \right)} + i \rho_{1316} \Omega{\left(16,7,0 \right)} - \frac{\rho_{1316}}{\tau} - i \rho_{416} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1317} = i \rho_{1317} \Omega{\left(17,8,0 \right)} - \frac{\rho_{1317}}{\tau} - i \rho_{417} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1318} = \Delta_{1318} \rho_{1318} - \frac{\rho_{1318}}{\tau} - i \rho_{418} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1319} = \Delta_{1319} \rho_{1319} + i \rho_{1319} \Omega{\left(19,4,0 \right)} - \frac{\rho_{1319}}{\tau} - i \rho_{419} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1320} = \Delta_{1320} \rho_{1320} + i \rho_{1320} \Omega{\left(20,5,0 \right)} - \frac{\rho_{1320}}{\tau} - i \rho_{420} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1321} = \Delta_{1321} \rho_{1321} + i \rho_{1321} \Omega{\left(21,6,0 \right)} - \frac{\rho_{1321}}{\tau} - i \rho_{421} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1322} = \Delta_{1322} \rho_{1322} + i \rho_{1322} \Omega{\left(22,7,0 \right)} - \frac{\rho_{1322}}{\tau} - i \rho_{422} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1323} = \Delta_{1323} \rho_{1323} + i \rho_{1323} \Omega{\left(23,8,0 \right)} - \frac{\rho_{1323}}{\tau} - i \rho_{423} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{1324} = \Delta_{1324} \rho_{1324} - \frac{\rho_{1324}}{\tau} - i \rho_{424} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{149} = \Delta_{149} \rho_{149} + i \rho_{149} \Omega{\left(9,2,0 \right)} - \frac{\rho_{149}}{\tau} - i \rho_{19} \Omega{\left(14,1,0 \right)} - i \rho_{59} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1410} = \Delta_{1410} \rho_{1410} - i \rho_{110} \Omega{\left(14,1,0 \right)} + i \rho_{1410} \Omega{\left(10,1,0 \right)} + i \rho_{1410} \Omega{\left(10,5,0 \right)} - \frac{\rho_{1410}}{\tau} - i \rho_{510} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1411} = \Delta_{1411} \rho_{1411} - i \rho_{111} \Omega{\left(14,1,0 \right)} + i \rho_{1411} \Omega{\left(11,6,0 \right)} - \frac{\rho_{1411}}{\tau} - i \rho_{511} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1412} = \Delta_{1412} \rho_{1412} - i \rho_{112} \Omega{\left(14,1,0 \right)} + i \rho_{1412} \Omega{\left(12,3,0 \right)} + i \rho_{1412} \Omega{\left(12,7,0 \right)} - \frac{\rho_{1412}}{\tau} - i \rho_{512} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1413} = - i \rho_{113} \Omega{\left(14,1,0 \right)} + i \rho_{1413} \Omega{\left(13,4,0 \right)} - \frac{\rho_{1413}}{\tau} - i \rho_{513} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1414} = - i \rho_{114} \Omega{\left(14,1,0 \right)} + i \rho_{1414} \Omega{\left(14,1,0 \right)} + i \rho_{1414} \Omega{\left(14,5,0 \right)} - \frac{\rho_{1414}}{\tau} - i \rho_{514} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1415} = - i \rho_{115} \Omega{\left(14,1,0 \right)} + i \rho_{1415} \Omega{\left(15,2,0 \right)} - \frac{\rho_{1415}}{\tau} - i \rho_{515} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1416} = - i \rho_{116} \Omega{\left(14,1,0 \right)} + i \rho_{1416} \Omega{\left(16,3,0 \right)} + i \rho_{1416} \Omega{\left(16,7,0 \right)} - \frac{\rho_{1416}}{\tau} - i \rho_{516} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1417} = - i \rho_{117} \Omega{\left(14,1,0 \right)} + i \rho_{1417} \Omega{\left(17,8,0 \right)} - \frac{\rho_{1417}}{\tau} - i \rho_{517} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1418} = \Delta_{1418} \rho_{1418} - i \rho_{118} \Omega{\left(14,1,0 \right)} - \frac{\rho_{1418}}{\tau} - i \rho_{518} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1419} = \Delta_{1419} \rho_{1419} - i \rho_{119} \Omega{\left(14,1,0 \right)} + i \rho_{1419} \Omega{\left(19,4,0 \right)} - \frac{\rho_{1419}}{\tau} - i \rho_{519} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1420} = \Delta_{1420} \rho_{1420} - i \rho_{120} \Omega{\left(14,1,0 \right)} + i \rho_{1420} \Omega{\left(20,5,0 \right)} - \frac{\rho_{1420}}{\tau} - i \rho_{520} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1421} = \Delta_{1421} \rho_{1421} - i \rho_{121} \Omega{\left(14,1,0 \right)} + i \rho_{1421} \Omega{\left(21,6,0 \right)} - \frac{\rho_{1421}}{\tau} - i \rho_{521} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1422} = \Delta_{1422} \rho_{1422} - i \rho_{122} \Omega{\left(14,1,0 \right)} + i \rho_{1422} \Omega{\left(22,7,0 \right)} - \frac{\rho_{1422}}{\tau} - i \rho_{522} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1423} = \Delta_{1423} \rho_{1423} - i \rho_{123} \Omega{\left(14,1,0 \right)} + i \rho_{1423} \Omega{\left(23,8,0 \right)} - \frac{\rho_{1423}}{\tau} - i \rho_{523} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{1424} = \Delta_{1424} \rho_{1424} - i \rho_{124} \Omega{\left(14,1,0 \right)} - \frac{\rho_{1424}}{\tau} - i \rho_{524} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{159} = \Delta_{159} \rho_{159} + i \rho_{159} \Omega{\left(9,2,0 \right)} - \frac{\rho_{159}}{\tau} - i \rho_{29} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1510} = \Delta_{1510} \rho_{1510} + i \rho_{1510} \Omega{\left(10,1,0 \right)} + i \rho_{1510} \Omega{\left(10,5,0 \right)} - \frac{\rho_{1510}}{\tau} - i \rho_{210} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1511} = \Delta_{1511} \rho_{1511} + i \rho_{1511} \Omega{\left(11,6,0 \right)} - \frac{\rho_{1511}}{\tau} - i \rho_{211} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1512} = \Delta_{1512} \rho_{1512} + i \rho_{1512} \Omega{\left(12,3,0 \right)} + i \rho_{1512} \Omega{\left(12,7,0 \right)} - \frac{\rho_{1512}}{\tau} - i \rho_{212} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1513} = i \rho_{1513} \Omega{\left(13,4,0 \right)} - \frac{\rho_{1513}}{\tau} - i \rho_{213} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1514} = i \rho_{1514} \Omega{\left(14,1,0 \right)} + i \rho_{1514} \Omega{\left(14,5,0 \right)} - \frac{\rho_{1514}}{\tau} - i \rho_{214} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1515} = i \rho_{1515} \Omega{\left(15,2,0 \right)} - \frac{\rho_{1515}}{\tau} - i \rho_{215} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1516} = i \rho_{1516} \Omega{\left(16,3,0 \right)} + i \rho_{1516} \Omega{\left(16,7,0 \right)} - \frac{\rho_{1516}}{\tau} - i \rho_{216} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1517} = i \rho_{1517} \Omega{\left(17,8,0 \right)} - \frac{\rho_{1517}}{\tau} - i \rho_{217} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1518} = \Delta_{1518} \rho_{1518} - \frac{\rho_{1518}}{\tau} - i \rho_{218} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1519} = \Delta_{1519} \rho_{1519} + i \rho_{1519} \Omega{\left(19,4,0 \right)} - \frac{\rho_{1519}}{\tau} - i \rho_{219} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1520} = \Delta_{1520} \rho_{1520} + i \rho_{1520} \Omega{\left(20,5,0 \right)} - \frac{\rho_{1520}}{\tau} - i \rho_{220} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1521} = \Delta_{1521} \rho_{1521} + i \rho_{1521} \Omega{\left(21,6,0 \right)} - \frac{\rho_{1521}}{\tau} - i \rho_{221} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1522} = \Delta_{1522} \rho_{1522} + i \rho_{1522} \Omega{\left(22,7,0 \right)} - \frac{\rho_{1522}}{\tau} - i \rho_{222} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1523} = \Delta_{1523} \rho_{1523} + i \rho_{1523} \Omega{\left(23,8,0 \right)} - \frac{\rho_{1523}}{\tau} - i \rho_{223} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{1524} = \Delta_{1524} \rho_{1524} - \frac{\rho_{1524}}{\tau} - i \rho_{224} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{169} = \Delta_{169} \rho_{169} + i \rho_{169} \Omega{\left(9,2,0 \right)} - \frac{\rho_{169}}{\tau} - i \rho_{39} \Omega{\left(16,3,0 \right)} - i \rho_{79} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1610} = \Delta_{1610} \rho_{1610} + i \rho_{1610} \Omega{\left(10,1,0 \right)} + i \rho_{1610} \Omega{\left(10,5,0 \right)} - \frac{\rho_{1610}}{\tau} - i \rho_{310} \Omega{\left(16,3,0 \right)} - i \rho_{710} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1611} = \Delta_{1611} \rho_{1611} + i \rho_{1611} \Omega{\left(11,6,0 \right)} - \frac{\rho_{1611}}{\tau} - i \rho_{311} \Omega{\left(16,3,0 \right)} - i \rho_{711} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1612} = \Delta_{1612} \rho_{1612} + i \rho_{1612} \Omega{\left(12,3,0 \right)} + i \rho_{1612} \Omega{\left(12,7,0 \right)} - \frac{\rho_{1612}}{\tau} - i \rho_{312} \Omega{\left(16,3,0 \right)} - i \rho_{712} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1613} = i \rho_{1613} \Omega{\left(13,4,0 \right)} - \frac{\rho_{1613}}{\tau} - i \rho_{313} \Omega{\left(16,3,0 \right)} - i \rho_{713} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1614} = i \rho_{1614} \Omega{\left(14,1,0 \right)} + i \rho_{1614} \Omega{\left(14,5,0 \right)} - \frac{\rho_{1614}}{\tau} - i \rho_{314} \Omega{\left(16,3,0 \right)} - i \rho_{714} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1615} = i \rho_{1615} \Omega{\left(15,2,0 \right)} - \frac{\rho_{1615}}{\tau} - i \rho_{315} \Omega{\left(16,3,0 \right)} - i \rho_{715} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1616} = i \rho_{1616} \Omega{\left(16,3,0 \right)} + i \rho_{1616} \Omega{\left(16,7,0 \right)} - \frac{\rho_{1616}}{\tau} - i \rho_{316} \Omega{\left(16,3,0 \right)} - i \rho_{716} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1617} = i \rho_{1617} \Omega{\left(17,8,0 \right)} - \frac{\rho_{1617}}{\tau} - i \rho_{317} \Omega{\left(16,3,0 \right)} - i \rho_{717} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1618} = \Delta_{1618} \rho_{1618} - \frac{\rho_{1618}}{\tau} - i \rho_{318} \Omega{\left(16,3,0 \right)} - i \rho_{718} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1619} = \Delta_{1619} \rho_{1619} + i \rho_{1619} \Omega{\left(19,4,0 \right)} - \frac{\rho_{1619}}{\tau} - i \rho_{319} \Omega{\left(16,3,0 \right)} - i \rho_{719} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1620} = \Delta_{1620} \rho_{1620} + i \rho_{1620} \Omega{\left(20,5,0 \right)} - \frac{\rho_{1620}}{\tau} - i \rho_{320} \Omega{\left(16,3,0 \right)} - i \rho_{720} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1621} = \Delta_{1621} \rho_{1621} + i \rho_{1621} \Omega{\left(21,6,0 \right)} - \frac{\rho_{1621}}{\tau} - i \rho_{321} \Omega{\left(16,3,0 \right)} - i \rho_{721} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1622} = \Delta_{1622} \rho_{1622} + i \rho_{1622} \Omega{\left(22,7,0 \right)} - \frac{\rho_{1622}}{\tau} - i \rho_{322} \Omega{\left(16,3,0 \right)} - i \rho_{722} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1623} = \Delta_{1623} \rho_{1623} + i \rho_{1623} \Omega{\left(23,8,0 \right)} - \frac{\rho_{1623}}{\tau} - i \rho_{323} \Omega{\left(16,3,0 \right)} - i \rho_{723} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{1624} = \Delta_{1624} \rho_{1624} - \frac{\rho_{1624}}{\tau} - i \rho_{324} \Omega{\left(16,3,0 \right)} - i \rho_{724} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{179} = \Delta_{179} \rho_{179} + i \rho_{179} \Omega{\left(9,2,0 \right)} - \frac{\rho_{179}}{\tau} - i \rho_{89} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1710} = \Delta_{1710} \rho_{1710} + i \rho_{1710} \Omega{\left(10,1,0 \right)} + i \rho_{1710} \Omega{\left(10,5,0 \right)} - \frac{\rho_{1710}}{\tau} - i \rho_{810} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1711} = \Delta_{1711} \rho_{1711} + i \rho_{1711} \Omega{\left(11,6,0 \right)} - \frac{\rho_{1711}}{\tau} - i \rho_{811} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1712} = \Delta_{1712} \rho_{1712} + i \rho_{1712} \Omega{\left(12,3,0 \right)} + i \rho_{1712} \Omega{\left(12,7,0 \right)} - \frac{\rho_{1712}}{\tau} - i \rho_{812} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1713} = i \rho_{1713} \Omega{\left(13,4,0 \right)} - \frac{\rho_{1713}}{\tau} - i \rho_{813} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1714} = i \rho_{1714} \Omega{\left(14,1,0 \right)} + i \rho_{1714} \Omega{\left(14,5,0 \right)} - \frac{\rho_{1714}}{\tau} - i \rho_{814} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1715} = i \rho_{1715} \Omega{\left(15,2,0 \right)} - \frac{\rho_{1715}}{\tau} - i \rho_{815} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1716} = i \rho_{1716} \Omega{\left(16,3,0 \right)} + i \rho_{1716} \Omega{\left(16,7,0 \right)} - \frac{\rho_{1716}}{\tau} - i \rho_{816} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1717} = i \rho_{1717} \Omega{\left(17,8,0 \right)} - \frac{\rho_{1717}}{\tau} - i \rho_{817} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1718} = \Delta_{1718} \rho_{1718} - \frac{\rho_{1718}}{\tau} - i \rho_{818} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1719} = \Delta_{1719} \rho_{1719} + i \rho_{1719} \Omega{\left(19,4,0 \right)} - \frac{\rho_{1719}}{\tau} - i \rho_{819} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1720} = \Delta_{1720} \rho_{1720} + i \rho_{1720} \Omega{\left(20,5,0 \right)} - \frac{\rho_{1720}}{\tau} - i \rho_{820} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1721} = \Delta_{1721} \rho_{1721} + i \rho_{1721} \Omega{\left(21,6,0 \right)} - \frac{\rho_{1721}}{\tau} - i \rho_{821} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1722} = \Delta_{1722} \rho_{1722} + i \rho_{1722} \Omega{\left(22,7,0 \right)} - \frac{\rho_{1722}}{\tau} - i \rho_{822} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1723} = \Delta_{1723} \rho_{1723} + i \rho_{1723} \Omega{\left(23,8,0 \right)} - \frac{\rho_{1723}}{\tau} - i \rho_{823} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{1724} = \Delta_{1724} \rho_{1724} - \frac{\rho_{1724}}{\tau} - i \rho_{824} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{189} = \Delta_{189} \rho_{189} + i \rho_{189} \Omega{\left(9,2,0 \right)} - \frac{\rho_{189}}{\tau}$

$\displaystyle \dot{\rho}_{1810} = \Delta_{1810} \rho_{1810} + i \rho_{1810} \Omega{\left(10,1,0 \right)} + i \rho_{1810} \Omega{\left(10,5,0 \right)} - \frac{\rho_{1810}}{\tau}$

$\displaystyle \dot{\rho}_{1811} = \Delta_{1811} \rho_{1811} + i \rho_{1811} \Omega{\left(11,6,0 \right)} - \frac{\rho_{1811}}{\tau}$

$\displaystyle \dot{\rho}_{1812} = \Delta_{1812} \rho_{1812} + i \rho_{1812} \Omega{\left(12,3,0 \right)} + i \rho_{1812} \Omega{\left(12,7,0 \right)} - \frac{\rho_{1812}}{\tau}$

$\displaystyle \dot{\rho}_{1813} = \Delta_{1813} \rho_{1813} + i \rho_{1813} \Omega{\left(13,4,0 \right)} - \frac{\rho_{1813}}{\tau}$

$\displaystyle \dot{\rho}_{1814} = \Delta_{1814} \rho_{1814} + i \rho_{1814} \Omega{\left(14,1,0 \right)} + i \rho_{1814} \Omega{\left(14,5,0 \right)} - \frac{\rho_{1814}}{\tau}$

$\displaystyle \dot{\rho}_{1815} = \Delta_{1815} \rho_{1815} + i \rho_{1815} \Omega{\left(15,2,0 \right)} - \frac{\rho_{1815}}{\tau}$

$\displaystyle \dot{\rho}_{1816} = \Delta_{1816} \rho_{1816} + i \rho_{1816} \Omega{\left(16,3,0 \right)} + i \rho_{1816} \Omega{\left(16,7,0 \right)} - \frac{\rho_{1816}}{\tau}$

$\displaystyle \dot{\rho}_{1817} = \Delta_{1817} \rho_{1817} + i \rho_{1817} \Omega{\left(17,8,0 \right)} - \frac{\rho_{1817}}{\tau}$

$\displaystyle \dot{\rho}_{1818} = - \frac{\rho_{1818}}{\tau}$

$\displaystyle \dot{\rho}_{1819} = i \rho_{1819} \Omega{\left(19,4,0 \right)} - \frac{\rho_{1819}}{\tau}$

$\displaystyle \dot{\rho}_{1820} = i \rho_{1820} \Omega{\left(20,5,0 \right)} - \frac{\rho_{1820}}{\tau}$

$\displaystyle \dot{\rho}_{1821} = i \rho_{1821} \Omega{\left(21,6,0 \right)} - \frac{\rho_{1821}}{\tau}$

$\displaystyle \dot{\rho}_{1822} = i \rho_{1822} \Omega{\left(22,7,0 \right)} - \frac{\rho_{1822}}{\tau}$

$\displaystyle \dot{\rho}_{1823} = i \rho_{1823} \Omega{\left(23,8,0 \right)} - \frac{\rho_{1823}}{\tau}$

$\displaystyle \dot{\rho}_{1824} = - \frac{\rho_{1824}}{\tau}$

$\displaystyle \dot{\rho}_{199} = \Delta_{199} \rho_{199} + i \rho_{199} \Omega{\left(9,2,0 \right)} - \frac{\rho_{199}}{\tau} - i \rho_{49} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1910} = \Delta_{1910} \rho_{1910} + i \rho_{1910} \Omega{\left(10,1,0 \right)} + i \rho_{1910} \Omega{\left(10,5,0 \right)} - \frac{\rho_{1910}}{\tau} - i \rho_{410} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1911} = \Delta_{1911} \rho_{1911} + i \rho_{1911} \Omega{\left(11,6,0 \right)} - \frac{\rho_{1911}}{\tau} - i \rho_{411} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1912} = \Delta_{1912} \rho_{1912} + i \rho_{1912} \Omega{\left(12,3,0 \right)} + i \rho_{1912} \Omega{\left(12,7,0 \right)} - \frac{\rho_{1912}}{\tau} - i \rho_{412} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1913} = \Delta_{1913} \rho_{1913} + i \rho_{1913} \Omega{\left(13,4,0 \right)} - \frac{\rho_{1913}}{\tau} - i \rho_{413} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1914} = \Delta_{1914} \rho_{1914} + i \rho_{1914} \Omega{\left(14,1,0 \right)} + i \rho_{1914} \Omega{\left(14,5,0 \right)} - \frac{\rho_{1914}}{\tau} - i \rho_{414} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1915} = \Delta_{1915} \rho_{1915} + i \rho_{1915} \Omega{\left(15,2,0 \right)} - \frac{\rho_{1915}}{\tau} - i \rho_{415} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1916} = \Delta_{1916} \rho_{1916} + i \rho_{1916} \Omega{\left(16,3,0 \right)} + i \rho_{1916} \Omega{\left(16,7,0 \right)} - \frac{\rho_{1916}}{\tau} - i \rho_{416} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1917} = \Delta_{1917} \rho_{1917} + i \rho_{1917} \Omega{\left(17,8,0 \right)} - \frac{\rho_{1917}}{\tau} - i \rho_{417} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1918} = - \frac{\rho_{1918}}{\tau} - i \rho_{418} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1919} = i \rho_{1919} \Omega{\left(19,4,0 \right)} - \frac{\rho_{1919}}{\tau} - i \rho_{419} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1920} = i \rho_{1920} \Omega{\left(20,5,0 \right)} - \frac{\rho_{1920}}{\tau} - i \rho_{420} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1921} = i \rho_{1921} \Omega{\left(21,6,0 \right)} - \frac{\rho_{1921}}{\tau} - i \rho_{421} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1922} = i \rho_{1922} \Omega{\left(22,7,0 \right)} - \frac{\rho_{1922}}{\tau} - i \rho_{422} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1923} = i \rho_{1923} \Omega{\left(23,8,0 \right)} - \frac{\rho_{1923}}{\tau} - i \rho_{423} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{1924} = - \frac{\rho_{1924}}{\tau} - i \rho_{424} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{209} = \Delta_{209} \rho_{209} + i \rho_{209} \Omega{\left(9,2,0 \right)} - \frac{\rho_{209}}{\tau} - i \rho_{59} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2010} = \Delta_{2010} \rho_{2010} + i \rho_{2010} \Omega{\left(10,1,0 \right)} + i \rho_{2010} \Omega{\left(10,5,0 \right)} - \frac{\rho_{2010}}{\tau} - i \rho_{510} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2011} = \Delta_{2011} \rho_{2011} + i \rho_{2011} \Omega{\left(11,6,0 \right)} - \frac{\rho_{2011}}{\tau} - i \rho_{511} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2012} = \Delta_{2012} \rho_{2012} + i \rho_{2012} \Omega{\left(12,3,0 \right)} + i \rho_{2012} \Omega{\left(12,7,0 \right)} - \frac{\rho_{2012}}{\tau} - i \rho_{512} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2013} = \Delta_{2013} \rho_{2013} + i \rho_{2013} \Omega{\left(13,4,0 \right)} - \frac{\rho_{2013}}{\tau} - i \rho_{513} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2014} = \Delta_{2014} \rho_{2014} + i \rho_{2014} \Omega{\left(14,1,0 \right)} + i \rho_{2014} \Omega{\left(14,5,0 \right)} - \frac{\rho_{2014}}{\tau} - i \rho_{514} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2015} = \Delta_{2015} \rho_{2015} + i \rho_{2015} \Omega{\left(15,2,0 \right)} - \frac{\rho_{2015}}{\tau} - i \rho_{515} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2016} = \Delta_{2016} \rho_{2016} + i \rho_{2016} \Omega{\left(16,3,0 \right)} + i \rho_{2016} \Omega{\left(16,7,0 \right)} - \frac{\rho_{2016}}{\tau} - i \rho_{516} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2017} = \Delta_{2017} \rho_{2017} + i \rho_{2017} \Omega{\left(17,8,0 \right)} - \frac{\rho_{2017}}{\tau} - i \rho_{517} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2018} = - \frac{\rho_{2018}}{\tau} - i \rho_{518} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2019} = i \rho_{2019} \Omega{\left(19,4,0 \right)} - \frac{\rho_{2019}}{\tau} - i \rho_{519} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2020} = i \rho_{2020} \Omega{\left(20,5,0 \right)} - \frac{\rho_{2020}}{\tau} - i \rho_{520} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2021} = i \rho_{2021} \Omega{\left(21,6,0 \right)} - \frac{\rho_{2021}}{\tau} - i \rho_{521} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2022} = i \rho_{2022} \Omega{\left(22,7,0 \right)} - \frac{\rho_{2022}}{\tau} - i \rho_{522} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2023} = i \rho_{2023} \Omega{\left(23,8,0 \right)} - \frac{\rho_{2023}}{\tau} - i \rho_{523} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{2024} = - \frac{\rho_{2024}}{\tau} - i \rho_{524} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{219} = \Delta_{219} \rho_{219} + i \rho_{219} \Omega{\left(9,2,0 \right)} - \frac{\rho_{219}}{\tau} - i \rho_{69} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2110} = \Delta_{2110} \rho_{2110} + i \rho_{2110} \Omega{\left(10,1,0 \right)} + i \rho_{2110} \Omega{\left(10,5,0 \right)} - \frac{\rho_{2110}}{\tau} - i \rho_{610} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2111} = \Delta_{2111} \rho_{2111} + i \rho_{2111} \Omega{\left(11,6,0 \right)} - \frac{\rho_{2111}}{\tau} - i \rho_{611} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2112} = \Delta_{2112} \rho_{2112} + i \rho_{2112} \Omega{\left(12,3,0 \right)} + i \rho_{2112} \Omega{\left(12,7,0 \right)} - \frac{\rho_{2112}}{\tau} - i \rho_{612} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2113} = \Delta_{2113} \rho_{2113} + i \rho_{2113} \Omega{\left(13,4,0 \right)} - \frac{\rho_{2113}}{\tau} - i \rho_{613} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2114} = \Delta_{2114} \rho_{2114} + i \rho_{2114} \Omega{\left(14,1,0 \right)} + i \rho_{2114} \Omega{\left(14,5,0 \right)} - \frac{\rho_{2114}}{\tau} - i \rho_{614} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2115} = \Delta_{2115} \rho_{2115} + i \rho_{2115} \Omega{\left(15,2,0 \right)} - \frac{\rho_{2115}}{\tau} - i \rho_{615} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2116} = \Delta_{2116} \rho_{2116} + i \rho_{2116} \Omega{\left(16,3,0 \right)} + i \rho_{2116} \Omega{\left(16,7,0 \right)} - \frac{\rho_{2116}}{\tau} - i \rho_{616} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2117} = \Delta_{2117} \rho_{2117} + i \rho_{2117} \Omega{\left(17,8,0 \right)} - \frac{\rho_{2117}}{\tau} - i \rho_{617} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2118} = - \frac{\rho_{2118}}{\tau} - i \rho_{618} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2119} = i \rho_{2119} \Omega{\left(19,4,0 \right)} - \frac{\rho_{2119}}{\tau} - i \rho_{619} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2120} = i \rho_{2120} \Omega{\left(20,5,0 \right)} - \frac{\rho_{2120}}{\tau} - i \rho_{620} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2121} = i \rho_{2121} \Omega{\left(21,6,0 \right)} - \frac{\rho_{2121}}{\tau} - i \rho_{621} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2122} = i \rho_{2122} \Omega{\left(22,7,0 \right)} - \frac{\rho_{2122}}{\tau} - i \rho_{622} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2123} = i \rho_{2123} \Omega{\left(23,8,0 \right)} - \frac{\rho_{2123}}{\tau} - i \rho_{623} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{2124} = - \frac{\rho_{2124}}{\tau} - i \rho_{624} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{229} = \Delta_{229} \rho_{229} + i \rho_{229} \Omega{\left(9,2,0 \right)} - \frac{\rho_{229}}{\tau} - i \rho_{79} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2210} = \Delta_{2210} \rho_{2210} + i \rho_{2210} \Omega{\left(10,1,0 \right)} + i \rho_{2210} \Omega{\left(10,5,0 \right)} - \frac{\rho_{2210}}{\tau} - i \rho_{710} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2211} = \Delta_{2211} \rho_{2211} + i \rho_{2211} \Omega{\left(11,6,0 \right)} - \frac{\rho_{2211}}{\tau} - i \rho_{711} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2212} = \Delta_{2212} \rho_{2212} + i \rho_{2212} \Omega{\left(12,3,0 \right)} + i \rho_{2212} \Omega{\left(12,7,0 \right)} - \frac{\rho_{2212}}{\tau} - i \rho_{712} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2213} = \Delta_{2213} \rho_{2213} + i \rho_{2213} \Omega{\left(13,4,0 \right)} - \frac{\rho_{2213}}{\tau} - i \rho_{713} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2214} = \Delta_{2214} \rho_{2214} + i \rho_{2214} \Omega{\left(14,1,0 \right)} + i \rho_{2214} \Omega{\left(14,5,0 \right)} - \frac{\rho_{2214}}{\tau} - i \rho_{714} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2215} = \Delta_{2215} \rho_{2215} + i \rho_{2215} \Omega{\left(15,2,0 \right)} - \frac{\rho_{2215}}{\tau} - i \rho_{715} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2216} = \Delta_{2216} \rho_{2216} + i \rho_{2216} \Omega{\left(16,3,0 \right)} + i \rho_{2216} \Omega{\left(16,7,0 \right)} - \frac{\rho_{2216}}{\tau} - i \rho_{716} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2217} = \Delta_{2217} \rho_{2217} + i \rho_{2217} \Omega{\left(17,8,0 \right)} - \frac{\rho_{2217}}{\tau} - i \rho_{717} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2218} = - \frac{\rho_{2218}}{\tau} - i \rho_{718} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2219} = i \rho_{2219} \Omega{\left(19,4,0 \right)} - \frac{\rho_{2219}}{\tau} - i \rho_{719} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2220} = i \rho_{2220} \Omega{\left(20,5,0 \right)} - \frac{\rho_{2220}}{\tau} - i \rho_{720} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2221} = i \rho_{2221} \Omega{\left(21,6,0 \right)} - \frac{\rho_{2221}}{\tau} - i \rho_{721} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2222} = i \rho_{2222} \Omega{\left(22,7,0 \right)} - \frac{\rho_{2222}}{\tau} - i \rho_{722} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2223} = i \rho_{2223} \Omega{\left(23,8,0 \right)} - \frac{\rho_{2223}}{\tau} - i \rho_{723} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{2224} = - \frac{\rho_{2224}}{\tau} - i \rho_{724} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{239} = \Delta_{239} \rho_{239} + i \rho_{239} \Omega{\left(9,2,0 \right)} - \frac{\rho_{239}}{\tau} - i \rho_{89} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2310} = \Delta_{2310} \rho_{2310} + i \rho_{2310} \Omega{\left(10,1,0 \right)} + i \rho_{2310} \Omega{\left(10,5,0 \right)} - \frac{\rho_{2310}}{\tau} - i \rho_{810} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2311} = \Delta_{2311} \rho_{2311} + i \rho_{2311} \Omega{\left(11,6,0 \right)} - \frac{\rho_{2311}}{\tau} - i \rho_{811} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2312} = \Delta_{2312} \rho_{2312} + i \rho_{2312} \Omega{\left(12,3,0 \right)} + i \rho_{2312} \Omega{\left(12,7,0 \right)} - \frac{\rho_{2312}}{\tau} - i \rho_{812} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2313} = \Delta_{2313} \rho_{2313} + i \rho_{2313} \Omega{\left(13,4,0 \right)} - \frac{\rho_{2313}}{\tau} - i \rho_{813} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2314} = \Delta_{2314} \rho_{2314} + i \rho_{2314} \Omega{\left(14,1,0 \right)} + i \rho_{2314} \Omega{\left(14,5,0 \right)} - \frac{\rho_{2314}}{\tau} - i \rho_{814} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2315} = \Delta_{2315} \rho_{2315} + i \rho_{2315} \Omega{\left(15,2,0 \right)} - \frac{\rho_{2315}}{\tau} - i \rho_{815} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2316} = \Delta_{2316} \rho_{2316} + i \rho_{2316} \Omega{\left(16,3,0 \right)} + i \rho_{2316} \Omega{\left(16,7,0 \right)} - \frac{\rho_{2316}}{\tau} - i \rho_{816} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2317} = \Delta_{2317} \rho_{2317} + i \rho_{2317} \Omega{\left(17,8,0 \right)} - \frac{\rho_{2317}}{\tau} - i \rho_{817} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2318} = - \frac{\rho_{2318}}{\tau} - i \rho_{818} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2319} = i \rho_{2319} \Omega{\left(19,4,0 \right)} - \frac{\rho_{2319}}{\tau} - i \rho_{819} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2320} = i \rho_{2320} \Omega{\left(20,5,0 \right)} - \frac{\rho_{2320}}{\tau} - i \rho_{820} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2321} = i \rho_{2321} \Omega{\left(21,6,0 \right)} - \frac{\rho_{2321}}{\tau} - i \rho_{821} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2322} = i \rho_{2322} \Omega{\left(22,7,0 \right)} - \frac{\rho_{2322}}{\tau} - i \rho_{822} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2323} = i \rho_{2323} \Omega{\left(23,8,0 \right)} - \frac{\rho_{2323}}{\tau} - i \rho_{823} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{2324} = - \frac{\rho_{2324}}{\tau} - i \rho_{824} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{249} = \Delta_{249} \rho_{249} + i \rho_{249} \Omega{\left(9,2,0 \right)} - \frac{\rho_{249}}{\tau}$

$\displaystyle \dot{\rho}_{2410} = \Delta_{2410} \rho_{2410} + i \rho_{2410} \Omega{\left(10,1,0 \right)} + i \rho_{2410} \Omega{\left(10,5,0 \right)} - \frac{\rho_{2410}}{\tau}$

$\displaystyle \dot{\rho}_{2411} = \Delta_{2411} \rho_{2411} + i \rho_{2411} \Omega{\left(11,6,0 \right)} - \frac{\rho_{2411}}{\tau}$

$\displaystyle \dot{\rho}_{2412} = \Delta_{2412} \rho_{2412} + i \rho_{2412} \Omega{\left(12,3,0 \right)} + i \rho_{2412} \Omega{\left(12,7,0 \right)} - \frac{\rho_{2412}}{\tau}$

$\displaystyle \dot{\rho}_{2413} = \Delta_{2413} \rho_{2413} + i \rho_{2413} \Omega{\left(13,4,0 \right)} - \frac{\rho_{2413}}{\tau}$

$\displaystyle \dot{\rho}_{2414} = \Delta_{2414} \rho_{2414} + i \rho_{2414} \Omega{\left(14,1,0 \right)} + i \rho_{2414} \Omega{\left(14,5,0 \right)} - \frac{\rho_{2414}}{\tau}$

$\displaystyle \dot{\rho}_{2415} = \Delta_{2415} \rho_{2415} + i \rho_{2415} \Omega{\left(15,2,0 \right)} - \frac{\rho_{2415}}{\tau}$

$\displaystyle \dot{\rho}_{2416} = \Delta_{2416} \rho_{2416} + i \rho_{2416} \Omega{\left(16,3,0 \right)} + i \rho_{2416} \Omega{\left(16,7,0 \right)} - \frac{\rho_{2416}}{\tau}$

$\displaystyle \dot{\rho}_{2417} = \Delta_{2417} \rho_{2417} + i \rho_{2417} \Omega{\left(17,8,0 \right)} - \frac{\rho_{2417}}{\tau}$

$\displaystyle \dot{\rho}_{2418} = - \frac{\rho_{2418}}{\tau}$

$\displaystyle \dot{\rho}_{2419} = i \rho_{2419} \Omega{\left(19,4,0 \right)} - \frac{\rho_{2419}}{\tau}$

$\displaystyle \dot{\rho}_{2420} = i \rho_{2420} \Omega{\left(20,5,0 \right)} - \frac{\rho_{2420}}{\tau}$

$\displaystyle \dot{\rho}_{2421} = i \rho_{2421} \Omega{\left(21,6,0 \right)} - \frac{\rho_{2421}}{\tau}$

$\displaystyle \dot{\rho}_{2422} = i \rho_{2422} \Omega{\left(22,7,0 \right)} - \frac{\rho_{2422}}{\tau}$

$\displaystyle \dot{\rho}_{2423} = i \rho_{2423} \Omega{\left(23,8,0 \right)} - \frac{\rho_{2423}}{\tau}$

$\displaystyle \dot{\rho}_{2424} = - \frac{\rho_{2424}}{\tau}$

$\displaystyle \dot{\rho}_{19} = - i \rho_{109} \Omega{\left(10,1,0 \right)} - i \rho_{12} \Omega{\left(9,2,0 \right)} - i \rho_{149} \Omega{\left(14,1,0 \right)} - i \rho_{19} \Delta{\left(9,1,\omega_{q},v_{z} \right)} - \frac{\rho_{19}}{2 \tau}$

$\displaystyle \dot{\rho}_{110} = - i \rho_{1010} \Omega{\left(10,1,0 \right)} - i \rho_{11} \Omega{\left(10,1,0 \right)} - i \rho_{110} \Delta{\left(10,1,\omega_{q},v_{z} \right)} - \frac{\rho_{110}}{2 \tau} - i \rho_{1410} \Omega{\left(14,1,0 \right)} - i \rho_{15} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{111} = - i \rho_{1011} \Omega{\left(10,1,0 \right)} - i \rho_{111} \Delta{\left(11,1,\omega_{q},v_{z} \right)} - \frac{\rho_{111}}{2 \tau} - i \rho_{1411} \Omega{\left(14,1,0 \right)} - i \rho_{16} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{112} = - i \rho_{1012} \Omega{\left(10,1,0 \right)} - i \rho_{112} \Delta{\left(12,1,\omega_{q},v_{z} \right)} - \frac{\rho_{112}}{2 \tau} - i \rho_{13} \Omega{\left(12,3,0 \right)} - i \rho_{1412} \Omega{\left(14,1,0 \right)} - i \rho_{17} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{113} = - i \rho_{1013} \Omega{\left(10,1,0 \right)} - i \rho_{113} \Delta{\left(13,1,\omega_{q},v_{z} \right)} - \frac{\rho_{113}}{2 \tau} - i \rho_{14} \Omega{\left(13,4,0 \right)} - i \rho_{1413} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{114} = - i \rho_{1014} \Omega{\left(10,1,0 \right)} - i \rho_{11} \Omega{\left(14,1,0 \right)} - i \rho_{114} \Delta{\left(14,1,\omega_{q},v_{z} \right)} - \frac{\rho_{114}}{2 \tau} - i \rho_{1414} \Omega{\left(14,1,0 \right)} - i \rho_{15} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{115} = - i \rho_{1015} \Omega{\left(10,1,0 \right)} - i \rho_{115} \Delta{\left(15,1,\omega_{q},v_{z} \right)} - \frac{\rho_{115}}{2 \tau} - i \rho_{12} \Omega{\left(15,2,0 \right)} - i \rho_{1415} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{116} = - i \rho_{1016} \Omega{\left(10,1,0 \right)} - i \rho_{116} \Delta{\left(16,1,\omega_{q},v_{z} \right)} - \frac{\rho_{116}}{2 \tau} - i \rho_{13} \Omega{\left(16,3,0 \right)} - i \rho_{1416} \Omega{\left(14,1,0 \right)} - i \rho_{17} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{117} = - i \rho_{1017} \Omega{\left(10,1,0 \right)} - i \rho_{117} \Delta{\left(17,1,\omega_{q},v_{z} \right)} - \frac{\rho_{117}}{2 \tau} - i \rho_{1417} \Omega{\left(14,1,0 \right)} - i \rho_{18} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{118} = - i \rho_{1018} \Omega{\left(10,1,0 \right)} - i \rho_{118} \Delta{\left(18,1,\omega_{q},v_{z} \right)} - \frac{\rho_{118}}{2 \tau} - i \rho_{1418} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{119} = - i \rho_{1019} \Omega{\left(10,1,0 \right)} - i \rho_{119} \Delta{\left(19,1,\omega_{q},v_{z} \right)} - \frac{\rho_{119}}{2 \tau} - i \rho_{14} \Omega{\left(19,4,0 \right)} - i \rho_{1419} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{120} = - i \rho_{1020} \Omega{\left(10,1,0 \right)} - i \rho_{120} \Delta{\left(20,1,\omega_{q},v_{z} \right)} - \frac{\rho_{120}}{2 \tau} - i \rho_{1420} \Omega{\left(14,1,0 \right)} - i \rho_{15} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{121} = - i \rho_{1021} \Omega{\left(10,1,0 \right)} - i \rho_{121} \Delta{\left(21,1,\omega_{q},v_{z} \right)} - \frac{\rho_{121}}{2 \tau} - i \rho_{1421} \Omega{\left(14,1,0 \right)} - i \rho_{16} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{122} = - i \rho_{1022} \Omega{\left(10,1,0 \right)} - i \rho_{122} \Delta{\left(22,1,\omega_{q},v_{z} \right)} - \frac{\rho_{122}}{2 \tau} - i \rho_{1422} \Omega{\left(14,1,0 \right)} - i \rho_{17} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{123} = - i \rho_{1023} \Omega{\left(10,1,0 \right)} - i \rho_{123} \Delta{\left(23,1,\omega_{q},v_{z} \right)} - \frac{\rho_{123}}{2 \tau} - i \rho_{1423} \Omega{\left(14,1,0 \right)} - i \rho_{18} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{124} = - i \rho_{1024} \Omega{\left(10,1,0 \right)} - i \rho_{124} \Delta{\left(24,1,\omega_{q},v_{z} \right)} - \frac{\rho_{124}}{2 \tau} - i \rho_{1424} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{29} = - i \rho_{159} \Omega{\left(15,2,0 \right)} - i \rho_{22} \Omega{\left(9,2,0 \right)} - i \rho_{29} \Delta{\left(9,2,\omega_{q},v_{z} \right)} - \frac{\rho_{29}}{2 \tau} - i \rho_{99} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{210} = - i \rho_{1510} \Omega{\left(15,2,0 \right)} - i \rho_{21} \Omega{\left(10,1,0 \right)} - i \rho_{210} \Delta{\left(10,2,\omega_{q},v_{z} \right)} - \frac{\rho_{210}}{2 \tau} - i \rho_{25} \Omega{\left(10,5,0 \right)} - i \rho_{910} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{211} = - i \rho_{1511} \Omega{\left(15,2,0 \right)} - i \rho_{211} \Delta{\left(11,2,\omega_{q},v_{z} \right)} - \frac{\rho_{211}}{2 \tau} - i \rho_{26} \Omega{\left(11,6,0 \right)} - i \rho_{911} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{212} = - i \rho_{1512} \Omega{\left(15,2,0 \right)} - i \rho_{212} \Delta{\left(12,2,\omega_{q},v_{z} \right)} - \frac{\rho_{212}}{2 \tau} - i \rho_{23} \Omega{\left(12,3,0 \right)} - i \rho_{27} \Omega{\left(12,7,0 \right)} - i \rho_{912} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{213} = - i \rho_{1513} \Omega{\left(15,2,0 \right)} - i \rho_{213} \Delta{\left(13,2,\omega_{q},v_{z} \right)} - \frac{\rho_{213}}{2 \tau} - i \rho_{24} \Omega{\left(13,4,0 \right)} - i \rho_{913} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{214} = - i \rho_{1514} \Omega{\left(15,2,0 \right)} - i \rho_{21} \Omega{\left(14,1,0 \right)} - i \rho_{214} \Delta{\left(14,2,\omega_{q},v_{z} \right)} - \frac{\rho_{214}}{2 \tau} - i \rho_{25} \Omega{\left(14,5,0 \right)} - i \rho_{914} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{215} = - i \rho_{1515} \Omega{\left(15,2,0 \right)} - i \rho_{215} \Delta{\left(15,2,\omega_{q},v_{z} \right)} - \frac{\rho_{215}}{2 \tau} - i \rho_{22} \Omega{\left(15,2,0 \right)} - i \rho_{915} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{216} = - i \rho_{1516} \Omega{\left(15,2,0 \right)} - i \rho_{216} \Delta{\left(16,2,\omega_{q},v_{z} \right)} - \frac{\rho_{216}}{2 \tau} - i \rho_{23} \Omega{\left(16,3,0 \right)} - i \rho_{27} \Omega{\left(16,7,0 \right)} - i \rho_{916} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{217} = - i \rho_{1517} \Omega{\left(15,2,0 \right)} - i \rho_{217} \Delta{\left(17,2,\omega_{q},v_{z} \right)} - \frac{\rho_{217}}{2 \tau} - i \rho_{28} \Omega{\left(17,8,0 \right)} - i \rho_{917} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{218} = - i \rho_{1518} \Omega{\left(15,2,0 \right)} - i \rho_{218} \Delta{\left(18,2,\omega_{q},v_{z} \right)} - \frac{\rho_{218}}{2 \tau} - i \rho_{918} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{219} = - i \rho_{1519} \Omega{\left(15,2,0 \right)} - i \rho_{219} \Delta{\left(19,2,\omega_{q},v_{z} \right)} - \frac{\rho_{219}}{2 \tau} - i \rho_{24} \Omega{\left(19,4,0 \right)} - i \rho_{919} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{220} = - i \rho_{1520} \Omega{\left(15,2,0 \right)} - i \rho_{220} \Delta{\left(20,2,\omega_{q},v_{z} \right)} - \frac{\rho_{220}}{2 \tau} - i \rho_{25} \Omega{\left(20,5,0 \right)} - i \rho_{920} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{221} = - i \rho_{1521} \Omega{\left(15,2,0 \right)} - i \rho_{221} \Delta{\left(21,2,\omega_{q},v_{z} \right)} - \frac{\rho_{221}}{2 \tau} - i \rho_{26} \Omega{\left(21,6,0 \right)} - i \rho_{921} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{222} = - i \rho_{1522} \Omega{\left(15,2,0 \right)} - i \rho_{222} \Delta{\left(22,2,\omega_{q},v_{z} \right)} - \frac{\rho_{222}}{2 \tau} - i \rho_{27} \Omega{\left(22,7,0 \right)} - i \rho_{922} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{223} = - i \rho_{1523} \Omega{\left(15,2,0 \right)} - i \rho_{223} \Delta{\left(23,2,\omega_{q},v_{z} \right)} - \frac{\rho_{223}}{2 \tau} - i \rho_{28} \Omega{\left(23,8,0 \right)} - i \rho_{923} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{224} = - i \rho_{1524} \Omega{\left(15,2,0 \right)} - i \rho_{224} \Delta{\left(24,2,\omega_{q},v_{z} \right)} - \frac{\rho_{224}}{2 \tau} - i \rho_{924} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{39} = - i \rho_{129} \Omega{\left(12,3,0 \right)} - i \rho_{169} \Omega{\left(16,3,0 \right)} - i \rho_{32} \Omega{\left(9,2,0 \right)} - i \rho_{39} \Delta{\left(9,3,\omega_{q},v_{z} \right)} - \frac{\rho_{39}}{2 \tau}$

$\displaystyle \dot{\rho}_{310} = - i \rho_{1210} \Omega{\left(12,3,0 \right)} - i \rho_{1610} \Omega{\left(16,3,0 \right)} - i \rho_{31} \Omega{\left(10,1,0 \right)} - i \rho_{310} \Delta{\left(10,3,\omega_{q},v_{z} \right)} - \frac{\rho_{310}}{2 \tau} - i \rho_{35} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{311} = - i \rho_{1211} \Omega{\left(12,3,0 \right)} - i \rho_{1611} \Omega{\left(16,3,0 \right)} - i \rho_{311} \Delta{\left(11,3,\omega_{q},v_{z} \right)} - \frac{\rho_{311}}{2 \tau} - i \rho_{36} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{312} = - i \rho_{1212} \Omega{\left(12,3,0 \right)} - i \rho_{1612} \Omega{\left(16,3,0 \right)} - i \rho_{312} \Delta{\left(12,3,\omega_{q},v_{z} \right)} - \frac{\rho_{312}}{2 \tau} - i \rho_{33} \Omega{\left(12,3,0 \right)} - i \rho_{37} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{313} = - i \rho_{1213} \Omega{\left(12,3,0 \right)} - i \rho_{1613} \Omega{\left(16,3,0 \right)} - i \rho_{313} \Delta{\left(13,3,\omega_{q},v_{z} \right)} - \frac{\rho_{313}}{2 \tau} - i \rho_{34} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{314} = - i \rho_{1214} \Omega{\left(12,3,0 \right)} - i \rho_{1614} \Omega{\left(16,3,0 \right)} - i \rho_{31} \Omega{\left(14,1,0 \right)} - i \rho_{314} \Delta{\left(14,3,\omega_{q},v_{z} \right)} - \frac{\rho_{314}}{2 \tau} - i \rho_{35} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{315} = - i \rho_{1215} \Omega{\left(12,3,0 \right)} - i \rho_{1615} \Omega{\left(16,3,0 \right)} - i \rho_{315} \Delta{\left(15,3,\omega_{q},v_{z} \right)} - \frac{\rho_{315}}{2 \tau} - i \rho_{32} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{316} = - i \rho_{1216} \Omega{\left(12,3,0 \right)} - i \rho_{1616} \Omega{\left(16,3,0 \right)} - i \rho_{316} \Delta{\left(16,3,\omega_{q},v_{z} \right)} - \frac{\rho_{316}}{2 \tau} - i \rho_{33} \Omega{\left(16,3,0 \right)} - i \rho_{37} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{317} = - i \rho_{1217} \Omega{\left(12,3,0 \right)} - i \rho_{1617} \Omega{\left(16,3,0 \right)} - i \rho_{317} \Delta{\left(17,3,\omega_{q},v_{z} \right)} - \frac{\rho_{317}}{2 \tau} - i \rho_{38} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{318} = - i \rho_{1218} \Omega{\left(12,3,0 \right)} - i \rho_{1618} \Omega{\left(16,3,0 \right)} - i \rho_{318} \Delta{\left(18,3,\omega_{q},v_{z} \right)} - \frac{\rho_{318}}{2 \tau}$

$\displaystyle \dot{\rho}_{319} = - i \rho_{1219} \Omega{\left(12,3,0 \right)} - i \rho_{1619} \Omega{\left(16,3,0 \right)} - i \rho_{319} \Delta{\left(19,3,\omega_{q},v_{z} \right)} - \frac{\rho_{319}}{2 \tau} - i \rho_{34} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{320} = - i \rho_{1220} \Omega{\left(12,3,0 \right)} - i \rho_{1620} \Omega{\left(16,3,0 \right)} - i \rho_{320} \Delta{\left(20,3,\omega_{q},v_{z} \right)} - \frac{\rho_{320}}{2 \tau} - i \rho_{35} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{321} = - i \rho_{1221} \Omega{\left(12,3,0 \right)} - i \rho_{1621} \Omega{\left(16,3,0 \right)} - i \rho_{321} \Delta{\left(21,3,\omega_{q},v_{z} \right)} - \frac{\rho_{321}}{2 \tau} - i \rho_{36} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{322} = - i \rho_{1222} \Omega{\left(12,3,0 \right)} - i \rho_{1622} \Omega{\left(16,3,0 \right)} - i \rho_{322} \Delta{\left(22,3,\omega_{q},v_{z} \right)} - \frac{\rho_{322}}{2 \tau} - i \rho_{37} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{323} = - i \rho_{1223} \Omega{\left(12,3,0 \right)} - i \rho_{1623} \Omega{\left(16,3,0 \right)} - i \rho_{323} \Delta{\left(23,3,\omega_{q},v_{z} \right)} - \frac{\rho_{323}}{2 \tau} - i \rho_{38} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{324} = - i \rho_{1224} \Omega{\left(12,3,0 \right)} - i \rho_{1624} \Omega{\left(16,3,0 \right)} - i \rho_{324} \Delta{\left(24,3,\omega_{q},v_{z} \right)} - \frac{\rho_{324}}{2 \tau}$

$\displaystyle \dot{\rho}_{49} = - i \rho_{139} \Omega{\left(13,4,0 \right)} - i \rho_{199} \Omega{\left(19,4,0 \right)} - i \rho_{42} \Omega{\left(9,2,0 \right)} - i \rho_{49} \Delta{\left(9,4,\omega_{q},v_{z} \right)} - \frac{\rho_{49}}{2 \tau}$

$\displaystyle \dot{\rho}_{410} = - i \rho_{1310} \Omega{\left(13,4,0 \right)} - i \rho_{1910} \Omega{\left(19,4,0 \right)} - i \rho_{41} \Omega{\left(10,1,0 \right)} - i \rho_{410} \Delta{\left(10,4,\omega_{q},v_{z} \right)} - \frac{\rho_{410}}{2 \tau} - i \rho_{45} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{411} = - i \rho_{1311} \Omega{\left(13,4,0 \right)} - i \rho_{1911} \Omega{\left(19,4,0 \right)} - i \rho_{411} \Delta{\left(11,4,\omega_{q},v_{z} \right)} - \frac{\rho_{411}}{2 \tau} - i \rho_{46} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{412} = - i \rho_{1312} \Omega{\left(13,4,0 \right)} - i \rho_{1912} \Omega{\left(19,4,0 \right)} - i \rho_{412} \Delta{\left(12,4,\omega_{q},v_{z} \right)} - \frac{\rho_{412}}{2 \tau} - i \rho_{43} \Omega{\left(12,3,0 \right)} - i \rho_{47} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{413} = - i \rho_{1313} \Omega{\left(13,4,0 \right)} - i \rho_{1913} \Omega{\left(19,4,0 \right)} - i \rho_{413} \Delta{\left(13,4,\omega_{q},v_{z} \right)} - \frac{\rho_{413}}{2 \tau} - i \rho_{44} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{414} = - i \rho_{1314} \Omega{\left(13,4,0 \right)} - i \rho_{1914} \Omega{\left(19,4,0 \right)} - i \rho_{41} \Omega{\left(14,1,0 \right)} - i \rho_{414} \Delta{\left(14,4,\omega_{q},v_{z} \right)} - \frac{\rho_{414}}{2 \tau} - i \rho_{45} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{415} = - i \rho_{1315} \Omega{\left(13,4,0 \right)} - i \rho_{1915} \Omega{\left(19,4,0 \right)} - i \rho_{415} \Delta{\left(15,4,\omega_{q},v_{z} \right)} - \frac{\rho_{415}}{2 \tau} - i \rho_{42} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{416} = - i \rho_{1316} \Omega{\left(13,4,0 \right)} - i \rho_{1916} \Omega{\left(19,4,0 \right)} - i \rho_{416} \Delta{\left(16,4,\omega_{q},v_{z} \right)} - \frac{\rho_{416}}{2 \tau} - i \rho_{43} \Omega{\left(16,3,0 \right)} - i \rho_{47} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{417} = - i \rho_{1317} \Omega{\left(13,4,0 \right)} - i \rho_{1917} \Omega{\left(19,4,0 \right)} - i \rho_{417} \Delta{\left(17,4,\omega_{q},v_{z} \right)} - \frac{\rho_{417}}{2 \tau} - i \rho_{48} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{418} = - i \rho_{1318} \Omega{\left(13,4,0 \right)} - i \rho_{1918} \Omega{\left(19,4,0 \right)} - i \rho_{418} \Delta{\left(18,4,\omega_{q},v_{z} \right)} - \frac{\rho_{418}}{2 \tau}$

$\displaystyle \dot{\rho}_{419} = - i \rho_{1319} \Omega{\left(13,4,0 \right)} - i \rho_{1919} \Omega{\left(19,4,0 \right)} - i \rho_{419} \Delta{\left(19,4,\omega_{q},v_{z} \right)} - \frac{\rho_{419}}{2 \tau} - i \rho_{44} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{420} = - i \rho_{1320} \Omega{\left(13,4,0 \right)} - i \rho_{1920} \Omega{\left(19,4,0 \right)} - i \rho_{420} \Delta{\left(20,4,\omega_{q},v_{z} \right)} - \frac{\rho_{420}}{2 \tau} - i \rho_{45} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{421} = - i \rho_{1321} \Omega{\left(13,4,0 \right)} - i \rho_{1921} \Omega{\left(19,4,0 \right)} - i \rho_{421} \Delta{\left(21,4,\omega_{q},v_{z} \right)} - \frac{\rho_{421}}{2 \tau} - i \rho_{46} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{422} = - i \rho_{1322} \Omega{\left(13,4,0 \right)} - i \rho_{1922} \Omega{\left(19,4,0 \right)} - i \rho_{422} \Delta{\left(22,4,\omega_{q},v_{z} \right)} - \frac{\rho_{422}}{2 \tau} - i \rho_{47} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{423} = - i \rho_{1323} \Omega{\left(13,4,0 \right)} - i \rho_{1923} \Omega{\left(19,4,0 \right)} - i \rho_{423} \Delta{\left(23,4,\omega_{q},v_{z} \right)} - \frac{\rho_{423}}{2 \tau} - i \rho_{48} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{424} = - i \rho_{1324} \Omega{\left(13,4,0 \right)} - i \rho_{1924} \Omega{\left(19,4,0 \right)} - i \rho_{424} \Delta{\left(24,4,\omega_{q},v_{z} \right)} - \frac{\rho_{424}}{2 \tau}$

$\displaystyle \dot{\rho}_{59} = - i \rho_{109} \Omega{\left(10,5,0 \right)} - i \rho_{149} \Omega{\left(14,5,0 \right)} - i \rho_{209} \Omega{\left(20,5,0 \right)} - i \rho_{52} \Omega{\left(9,2,0 \right)} - i \rho_{59} \Delta{\left(9,5,\omega_{q},v_{z} \right)} - \frac{\rho_{59}}{2 \tau}$

$\displaystyle \dot{\rho}_{510} = - i \rho_{1010} \Omega{\left(10,5,0 \right)} - i \rho_{1410} \Omega{\left(14,5,0 \right)} - i \rho_{2010} \Omega{\left(20,5,0 \right)} - i \rho_{51} \Omega{\left(10,1,0 \right)} - i \rho_{510} \Delta{\left(10,5,\omega_{q},v_{z} \right)} - \frac{\rho_{510}}{2 \tau} - i \rho_{55} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{511} = - i \rho_{1011} \Omega{\left(10,5,0 \right)} - i \rho_{1411} \Omega{\left(14,5,0 \right)} - i \rho_{2011} \Omega{\left(20,5,0 \right)} - i \rho_{511} \Delta{\left(11,5,\omega_{q},v_{z} \right)} - \frac{\rho_{511}}{2 \tau} - i \rho_{56} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{512} = - i \rho_{1012} \Omega{\left(10,5,0 \right)} - i \rho_{1412} \Omega{\left(14,5,0 \right)} - i \rho_{2012} \Omega{\left(20,5,0 \right)} - i \rho_{512} \Delta{\left(12,5,\omega_{q},v_{z} \right)} - \frac{\rho_{512}}{2 \tau} - i \rho_{53} \Omega{\left(12,3,0 \right)} - i \rho_{57} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{513} = - i \rho_{1013} \Omega{\left(10,5,0 \right)} - i \rho_{1413} \Omega{\left(14,5,0 \right)} - i \rho_{2013} \Omega{\left(20,5,0 \right)} - i \rho_{513} \Delta{\left(13,5,\omega_{q},v_{z} \right)} - \frac{\rho_{513}}{2 \tau} - i \rho_{54} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{514} = - i \rho_{1014} \Omega{\left(10,5,0 \right)} - i \rho_{1414} \Omega{\left(14,5,0 \right)} - i \rho_{2014} \Omega{\left(20,5,0 \right)} - i \rho_{51} \Omega{\left(14,1,0 \right)} - i \rho_{514} \Delta{\left(14,5,\omega_{q},v_{z} \right)} - \frac{\rho_{514}}{2 \tau} - i \rho_{55} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{515} = - i \rho_{1015} \Omega{\left(10,5,0 \right)} - i \rho_{1415} \Omega{\left(14,5,0 \right)} - i \rho_{2015} \Omega{\left(20,5,0 \right)} - i \rho_{515} \Delta{\left(15,5,\omega_{q},v_{z} \right)} - \frac{\rho_{515}}{2 \tau} - i \rho_{52} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{516} = - i \rho_{1016} \Omega{\left(10,5,0 \right)} - i \rho_{1416} \Omega{\left(14,5,0 \right)} - i \rho_{2016} \Omega{\left(20,5,0 \right)} - i \rho_{516} \Delta{\left(16,5,\omega_{q},v_{z} \right)} - \frac{\rho_{516}}{2 \tau} - i \rho_{53} \Omega{\left(16,3,0 \right)} - i \rho_{57} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{517} = - i \rho_{1017} \Omega{\left(10,5,0 \right)} - i \rho_{1417} \Omega{\left(14,5,0 \right)} - i \rho_{2017} \Omega{\left(20,5,0 \right)} - i \rho_{517} \Delta{\left(17,5,\omega_{q},v_{z} \right)} - \frac{\rho_{517}}{2 \tau} - i \rho_{58} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{518} = - i \rho_{1018} \Omega{\left(10,5,0 \right)} - i \rho_{1418} \Omega{\left(14,5,0 \right)} - i \rho_{2018} \Omega{\left(20,5,0 \right)} - i \rho_{518} \Delta{\left(18,5,\omega_{q},v_{z} \right)} - \frac{\rho_{518}}{2 \tau}$

$\displaystyle \dot{\rho}_{519} = - i \rho_{1019} \Omega{\left(10,5,0 \right)} - i \rho_{1419} \Omega{\left(14,5,0 \right)} - i \rho_{2019} \Omega{\left(20,5,0 \right)} - i \rho_{519} \Delta{\left(19,5,\omega_{q},v_{z} \right)} - \frac{\rho_{519}}{2 \tau} - i \rho_{54} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{520} = - i \rho_{1020} \Omega{\left(10,5,0 \right)} - i \rho_{1420} \Omega{\left(14,5,0 \right)} - i \rho_{2020} \Omega{\left(20,5,0 \right)} - i \rho_{520} \Delta{\left(20,5,\omega_{q},v_{z} \right)} - \frac{\rho_{520}}{2 \tau} - i \rho_{55} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{521} = - i \rho_{1021} \Omega{\left(10,5,0 \right)} - i \rho_{1421} \Omega{\left(14,5,0 \right)} - i \rho_{2021} \Omega{\left(20,5,0 \right)} - i \rho_{521} \Delta{\left(21,5,\omega_{q},v_{z} \right)} - \frac{\rho_{521}}{2 \tau} - i \rho_{56} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{522} = - i \rho_{1022} \Omega{\left(10,5,0 \right)} - i \rho_{1422} \Omega{\left(14,5,0 \right)} - i \rho_{2022} \Omega{\left(20,5,0 \right)} - i \rho_{522} \Delta{\left(22,5,\omega_{q},v_{z} \right)} - \frac{\rho_{522}}{2 \tau} - i \rho_{57} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{523} = - i \rho_{1023} \Omega{\left(10,5,0 \right)} - i \rho_{1423} \Omega{\left(14,5,0 \right)} - i \rho_{2023} \Omega{\left(20,5,0 \right)} - i \rho_{523} \Delta{\left(23,5,\omega_{q},v_{z} \right)} - \frac{\rho_{523}}{2 \tau} - i \rho_{58} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{524} = - i \rho_{1024} \Omega{\left(10,5,0 \right)} - i \rho_{1424} \Omega{\left(14,5,0 \right)} - i \rho_{2024} \Omega{\left(20,5,0 \right)} - i \rho_{524} \Delta{\left(24,5,\omega_{q},v_{z} \right)} - \frac{\rho_{524}}{2 \tau}$

$\displaystyle \dot{\rho}_{69} = - i \rho_{119} \Omega{\left(11,6,0 \right)} - i \rho_{219} \Omega{\left(21,6,0 \right)} - i \rho_{62} \Omega{\left(9,2,0 \right)} - i \rho_{69} \Delta{\left(9,6,\omega_{q},v_{z} \right)} - \frac{\rho_{69}}{2 \tau}$

$\displaystyle \dot{\rho}_{610} = - i \rho_{1110} \Omega{\left(11,6,0 \right)} - i \rho_{2110} \Omega{\left(21,6,0 \right)} - i \rho_{61} \Omega{\left(10,1,0 \right)} - i \rho_{610} \Delta{\left(10,6,\omega_{q},v_{z} \right)} - \frac{\rho_{610}}{2 \tau} - i \rho_{65} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{611} = - i \rho_{1111} \Omega{\left(11,6,0 \right)} - i \rho_{2111} \Omega{\left(21,6,0 \right)} - i \rho_{611} \Delta{\left(11,6,\omega_{q},v_{z} \right)} - \frac{\rho_{611}}{2 \tau} - i \rho_{66} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{612} = - i \rho_{1112} \Omega{\left(11,6,0 \right)} - i \rho_{2112} \Omega{\left(21,6,0 \right)} - i \rho_{612} \Delta{\left(12,6,\omega_{q},v_{z} \right)} - \frac{\rho_{612}}{2 \tau} - i \rho_{63} \Omega{\left(12,3,0 \right)} - i \rho_{67} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{613} = - i \rho_{1113} \Omega{\left(11,6,0 \right)} - i \rho_{2113} \Omega{\left(21,6,0 \right)} - i \rho_{613} \Delta{\left(13,6,\omega_{q},v_{z} \right)} - \frac{\rho_{613}}{2 \tau} - i \rho_{64} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{614} = - i \rho_{1114} \Omega{\left(11,6,0 \right)} - i \rho_{2114} \Omega{\left(21,6,0 \right)} - i \rho_{61} \Omega{\left(14,1,0 \right)} - i \rho_{614} \Delta{\left(14,6,\omega_{q},v_{z} \right)} - \frac{\rho_{614}}{2 \tau} - i \rho_{65} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{615} = - i \rho_{1115} \Omega{\left(11,6,0 \right)} - i \rho_{2115} \Omega{\left(21,6,0 \right)} - i \rho_{615} \Delta{\left(15,6,\omega_{q},v_{z} \right)} - \frac{\rho_{615}}{2 \tau} - i \rho_{62} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{616} = - i \rho_{1116} \Omega{\left(11,6,0 \right)} - i \rho_{2116} \Omega{\left(21,6,0 \right)} - i \rho_{616} \Delta{\left(16,6,\omega_{q},v_{z} \right)} - \frac{\rho_{616}}{2 \tau} - i \rho_{63} \Omega{\left(16,3,0 \right)} - i \rho_{67} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{617} = - i \rho_{1117} \Omega{\left(11,6,0 \right)} - i \rho_{2117} \Omega{\left(21,6,0 \right)} - i \rho_{617} \Delta{\left(17,6,\omega_{q},v_{z} \right)} - \frac{\rho_{617}}{2 \tau} - i \rho_{68} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{618} = - i \rho_{1118} \Omega{\left(11,6,0 \right)} - i \rho_{2118} \Omega{\left(21,6,0 \right)} - i \rho_{618} \Delta{\left(18,6,\omega_{q},v_{z} \right)} - \frac{\rho_{618}}{2 \tau}$

$\displaystyle \dot{\rho}_{619} = - i \rho_{1119} \Omega{\left(11,6,0 \right)} - i \rho_{2119} \Omega{\left(21,6,0 \right)} - i \rho_{619} \Delta{\left(19,6,\omega_{q},v_{z} \right)} - \frac{\rho_{619}}{2 \tau} - i \rho_{64} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{620} = - i \rho_{1120} \Omega{\left(11,6,0 \right)} - i \rho_{2120} \Omega{\left(21,6,0 \right)} - i \rho_{620} \Delta{\left(20,6,\omega_{q},v_{z} \right)} - \frac{\rho_{620}}{2 \tau} - i \rho_{65} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{621} = - i \rho_{1121} \Omega{\left(11,6,0 \right)} - i \rho_{2121} \Omega{\left(21,6,0 \right)} - i \rho_{621} \Delta{\left(21,6,\omega_{q},v_{z} \right)} - \frac{\rho_{621}}{2 \tau} - i \rho_{66} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{622} = - i \rho_{1122} \Omega{\left(11,6,0 \right)} - i \rho_{2122} \Omega{\left(21,6,0 \right)} - i \rho_{622} \Delta{\left(22,6,\omega_{q},v_{z} \right)} - \frac{\rho_{622}}{2 \tau} - i \rho_{67} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{623} = - i \rho_{1123} \Omega{\left(11,6,0 \right)} - i \rho_{2123} \Omega{\left(21,6,0 \right)} - i \rho_{623} \Delta{\left(23,6,\omega_{q},v_{z} \right)} - \frac{\rho_{623}}{2 \tau} - i \rho_{68} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{624} = - i \rho_{1124} \Omega{\left(11,6,0 \right)} - i \rho_{2124} \Omega{\left(21,6,0 \right)} - i \rho_{624} \Delta{\left(24,6,\omega_{q},v_{z} \right)} - \frac{\rho_{624}}{2 \tau}$

$\displaystyle \dot{\rho}_{79} = - i \rho_{129} \Omega{\left(12,7,0 \right)} - i \rho_{169} \Omega{\left(16,7,0 \right)} - i \rho_{229} \Omega{\left(22,7,0 \right)} - i \rho_{72} \Omega{\left(9,2,0 \right)} - i \rho_{79} \Delta{\left(9,7,\omega_{q},v_{z} \right)} - \frac{\rho_{79}}{2 \tau}$

$\displaystyle \dot{\rho}_{710} = - i \rho_{1210} \Omega{\left(12,7,0 \right)} - i \rho_{1610} \Omega{\left(16,7,0 \right)} - i \rho_{2210} \Omega{\left(22,7,0 \right)} - i \rho_{71} \Omega{\left(10,1,0 \right)} - i \rho_{710} \Delta{\left(10,7,\omega_{q},v_{z} \right)} - \frac{\rho_{710}}{2 \tau} - i \rho_{75} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{711} = - i \rho_{1211} \Omega{\left(12,7,0 \right)} - i \rho_{1611} \Omega{\left(16,7,0 \right)} - i \rho_{2211} \Omega{\left(22,7,0 \right)} - i \rho_{711} \Delta{\left(11,7,\omega_{q},v_{z} \right)} - \frac{\rho_{711}}{2 \tau} - i \rho_{76} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{712} = - i \rho_{1212} \Omega{\left(12,7,0 \right)} - i \rho_{1612} \Omega{\left(16,7,0 \right)} - i \rho_{2212} \Omega{\left(22,7,0 \right)} - i \rho_{712} \Delta{\left(12,7,\omega_{q},v_{z} \right)} - \frac{\rho_{712}}{2 \tau} - i \rho_{73} \Omega{\left(12,3,0 \right)} - i \rho_{77} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{713} = - i \rho_{1213} \Omega{\left(12,7,0 \right)} - i \rho_{1613} \Omega{\left(16,7,0 \right)} - i \rho_{2213} \Omega{\left(22,7,0 \right)} - i \rho_{713} \Delta{\left(13,7,\omega_{q},v_{z} \right)} - \frac{\rho_{713}}{2 \tau} - i \rho_{74} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{714} = - i \rho_{1214} \Omega{\left(12,7,0 \right)} - i \rho_{1614} \Omega{\left(16,7,0 \right)} - i \rho_{2214} \Omega{\left(22,7,0 \right)} - i \rho_{71} \Omega{\left(14,1,0 \right)} - i \rho_{714} \Delta{\left(14,7,\omega_{q},v_{z} \right)} - \frac{\rho_{714}}{2 \tau} - i \rho_{75} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{715} = - i \rho_{1215} \Omega{\left(12,7,0 \right)} - i \rho_{1615} \Omega{\left(16,7,0 \right)} - i \rho_{2215} \Omega{\left(22,7,0 \right)} - i \rho_{715} \Delta{\left(15,7,\omega_{q},v_{z} \right)} - \frac{\rho_{715}}{2 \tau} - i \rho_{72} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{716} = - i \rho_{1216} \Omega{\left(12,7,0 \right)} - i \rho_{1616} \Omega{\left(16,7,0 \right)} - i \rho_{2216} \Omega{\left(22,7,0 \right)} - i \rho_{716} \Delta{\left(16,7,\omega_{q},v_{z} \right)} - \frac{\rho_{716}}{2 \tau} - i \rho_{73} \Omega{\left(16,3,0 \right)} - i \rho_{77} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{717} = - i \rho_{1217} \Omega{\left(12,7,0 \right)} - i \rho_{1617} \Omega{\left(16,7,0 \right)} - i \rho_{2217} \Omega{\left(22,7,0 \right)} - i \rho_{717} \Delta{\left(17,7,\omega_{q},v_{z} \right)} - \frac{\rho_{717}}{2 \tau} - i \rho_{78} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{718} = - i \rho_{1218} \Omega{\left(12,7,0 \right)} - i \rho_{1618} \Omega{\left(16,7,0 \right)} - i \rho_{2218} \Omega{\left(22,7,0 \right)} - i \rho_{718} \Delta{\left(18,7,\omega_{q},v_{z} \right)} - \frac{\rho_{718}}{2 \tau}$

$\displaystyle \dot{\rho}_{719} = - i \rho_{1219} \Omega{\left(12,7,0 \right)} - i \rho_{1619} \Omega{\left(16,7,0 \right)} - i \rho_{2219} \Omega{\left(22,7,0 \right)} - i \rho_{719} \Delta{\left(19,7,\omega_{q},v_{z} \right)} - \frac{\rho_{719}}{2 \tau} - i \rho_{74} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{720} = - i \rho_{1220} \Omega{\left(12,7,0 \right)} - i \rho_{1620} \Omega{\left(16,7,0 \right)} - i \rho_{2220} \Omega{\left(22,7,0 \right)} - i \rho_{720} \Delta{\left(20,7,\omega_{q},v_{z} \right)} - \frac{\rho_{720}}{2 \tau} - i \rho_{75} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{721} = - i \rho_{1221} \Omega{\left(12,7,0 \right)} - i \rho_{1621} \Omega{\left(16,7,0 \right)} - i \rho_{2221} \Omega{\left(22,7,0 \right)} - i \rho_{721} \Delta{\left(21,7,\omega_{q},v_{z} \right)} - \frac{\rho_{721}}{2 \tau} - i \rho_{76} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{722} = - i \rho_{1222} \Omega{\left(12,7,0 \right)} - i \rho_{1622} \Omega{\left(16,7,0 \right)} - i \rho_{2222} \Omega{\left(22,7,0 \right)} - i \rho_{722} \Delta{\left(22,7,\omega_{q},v_{z} \right)} - \frac{\rho_{722}}{2 \tau} - i \rho_{77} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{723} = - i \rho_{1223} \Omega{\left(12,7,0 \right)} - i \rho_{1623} \Omega{\left(16,7,0 \right)} - i \rho_{2223} \Omega{\left(22,7,0 \right)} - i \rho_{723} \Delta{\left(23,7,\omega_{q},v_{z} \right)} - \frac{\rho_{723}}{2 \tau} - i \rho_{78} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{724} = - i \rho_{1224} \Omega{\left(12,7,0 \right)} - i \rho_{1624} \Omega{\left(16,7,0 \right)} - i \rho_{2224} \Omega{\left(22,7,0 \right)} - i \rho_{724} \Delta{\left(24,7,\omega_{q},v_{z} \right)} - \frac{\rho_{724}}{2 \tau}$

$\displaystyle \dot{\rho}_{89} = - i \rho_{179} \Omega{\left(17,8,0 \right)} - i \rho_{239} \Omega{\left(23,8,0 \right)} - i \rho_{82} \Omega{\left(9,2,0 \right)} - i \rho_{89} \Delta{\left(9,8,\omega_{q},v_{z} \right)} - \frac{\rho_{89}}{2 \tau}$

$\displaystyle \dot{\rho}_{810} = - i \rho_{1710} \Omega{\left(17,8,0 \right)} - i \rho_{2310} \Omega{\left(23,8,0 \right)} - i \rho_{81} \Omega{\left(10,1,0 \right)} - i \rho_{810} \Delta{\left(10,8,\omega_{q},v_{z} \right)} - \frac{\rho_{810}}{2 \tau} - i \rho_{85} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{811} = - i \rho_{1711} \Omega{\left(17,8,0 \right)} - i \rho_{2311} \Omega{\left(23,8,0 \right)} - i \rho_{811} \Delta{\left(11,8,\omega_{q},v_{z} \right)} - \frac{\rho_{811}}{2 \tau} - i \rho_{86} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{812} = - i \rho_{1712} \Omega{\left(17,8,0 \right)} - i \rho_{2312} \Omega{\left(23,8,0 \right)} - i \rho_{812} \Delta{\left(12,8,\omega_{q},v_{z} \right)} - \frac{\rho_{812}}{2 \tau} - i \rho_{83} \Omega{\left(12,3,0 \right)} - i \rho_{87} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{813} = - i \rho_{1713} \Omega{\left(17,8,0 \right)} - i \rho_{2313} \Omega{\left(23,8,0 \right)} - i \rho_{813} \Delta{\left(13,8,\omega_{q},v_{z} \right)} - \frac{\rho_{813}}{2 \tau} - i \rho_{84} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{814} = - i \rho_{1714} \Omega{\left(17,8,0 \right)} - i \rho_{2314} \Omega{\left(23,8,0 \right)} - i \rho_{81} \Omega{\left(14,1,0 \right)} - i \rho_{814} \Delta{\left(14,8,\omega_{q},v_{z} \right)} - \frac{\rho_{814}}{2 \tau} - i \rho_{85} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{815} = - i \rho_{1715} \Omega{\left(17,8,0 \right)} - i \rho_{2315} \Omega{\left(23,8,0 \right)} - i \rho_{815} \Delta{\left(15,8,\omega_{q},v_{z} \right)} - \frac{\rho_{815}}{2 \tau} - i \rho_{82} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{816} = - i \rho_{1716} \Omega{\left(17,8,0 \right)} - i \rho_{2316} \Omega{\left(23,8,0 \right)} - i \rho_{816} \Delta{\left(16,8,\omega_{q},v_{z} \right)} - \frac{\rho_{816}}{2 \tau} - i \rho_{83} \Omega{\left(16,3,0 \right)} - i \rho_{87} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{817} = - i \rho_{1717} \Omega{\left(17,8,0 \right)} - i \rho_{2317} \Omega{\left(23,8,0 \right)} - i \rho_{817} \Delta{\left(17,8,\omega_{q},v_{z} \right)} - \frac{\rho_{817}}{2 \tau} - i \rho_{88} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{818} = - i \rho_{1718} \Omega{\left(17,8,0 \right)} - i \rho_{2318} \Omega{\left(23,8,0 \right)} - i \rho_{818} \Delta{\left(18,8,\omega_{q},v_{z} \right)} - \frac{\rho_{818}}{2 \tau}$

$\displaystyle \dot{\rho}_{819} = - i \rho_{1719} \Omega{\left(17,8,0 \right)} - i \rho_{2319} \Omega{\left(23,8,0 \right)} - i \rho_{819} \Delta{\left(19,8,\omega_{q},v_{z} \right)} - \frac{\rho_{819}}{2 \tau} - i \rho_{84} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{820} = - i \rho_{1720} \Omega{\left(17,8,0 \right)} - i \rho_{2320} \Omega{\left(23,8,0 \right)} - i \rho_{820} \Delta{\left(20,8,\omega_{q},v_{z} \right)} - \frac{\rho_{820}}{2 \tau} - i \rho_{85} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{821} = - i \rho_{1721} \Omega{\left(17,8,0 \right)} - i \rho_{2321} \Omega{\left(23,8,0 \right)} - i \rho_{821} \Delta{\left(21,8,\omega_{q},v_{z} \right)} - \frac{\rho_{821}}{2 \tau} - i \rho_{86} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{822} = - i \rho_{1722} \Omega{\left(17,8,0 \right)} - i \rho_{2322} \Omega{\left(23,8,0 \right)} - i \rho_{822} \Delta{\left(22,8,\omega_{q},v_{z} \right)} - \frac{\rho_{822}}{2 \tau} - i \rho_{87} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{823} = - i \rho_{1723} \Omega{\left(17,8,0 \right)} - i \rho_{2323} \Omega{\left(23,8,0 \right)} - i \rho_{823} \Delta{\left(23,8,\omega_{q},v_{z} \right)} - \frac{\rho_{823}}{2 \tau} - i \rho_{88} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{824} = - i \rho_{1724} \Omega{\left(17,8,0 \right)} - i \rho_{2324} \Omega{\left(23,8,0 \right)} - i \rho_{824} \Delta{\left(24,8,\omega_{q},v_{z} \right)} - \frac{\rho_{824}}{2 \tau}$

$\displaystyle \dot{\rho}_{91} = - i \rho_{91} \Delta{\left(9,1,\omega_{q},v_{z} \right)} - \frac{\rho_{91}}{2 \tau} + i \rho_{910} \Omega{\left(10,1,0 \right)} + i \rho_{914} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{92} = i \rho_{12} \Omega{\left(9,2,0 \right)} + i \rho_{22} \Omega{\left(9,2,0 \right)} + i \rho_{32} \Omega{\left(9,2,0 \right)} + i \rho_{42} \Omega{\left(9,2,0 \right)} + i \rho_{52} \Omega{\left(9,2,0 \right)} + i \rho_{62} \Omega{\left(9,2,0 \right)} + i \rho_{72} \Omega{\left(9,2,0 \right)} + i \rho_{82} \Omega{\left(9,2,0 \right)} + i \rho_{915} \Omega{\left(15,2,0 \right)} - i \rho_{92} \Delta{\left(9,2,\omega_{q},v_{z} \right)} - \frac{\rho_{92}}{2 \tau} + i \rho_{99} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{93} = i \rho_{912} \Omega{\left(12,3,0 \right)} + i \rho_{916} \Omega{\left(16,3,0 \right)} - i \rho_{93} \Delta{\left(9,3,\omega_{q},v_{z} \right)} - \frac{\rho_{93}}{2 \tau}$

$\displaystyle \dot{\rho}_{94} = i \rho_{913} \Omega{\left(13,4,0 \right)} + i \rho_{919} \Omega{\left(19,4,0 \right)} - i \rho_{94} \Delta{\left(9,4,\omega_{q},v_{z} \right)} - \frac{\rho_{94}}{2 \tau}$

$\displaystyle \dot{\rho}_{95} = i \rho_{910} \Omega{\left(10,5,0 \right)} + i \rho_{914} \Omega{\left(14,5,0 \right)} + i \rho_{920} \Omega{\left(20,5,0 \right)} - i \rho_{95} \Delta{\left(9,5,\omega_{q},v_{z} \right)} - \frac{\rho_{95}}{2 \tau}$

$\displaystyle \dot{\rho}_{96} = i \rho_{911} \Omega{\left(11,6,0 \right)} + i \rho_{921} \Omega{\left(21,6,0 \right)} - i \rho_{96} \Delta{\left(9,6,\omega_{q},v_{z} \right)} - \frac{\rho_{96}}{2 \tau}$

$\displaystyle \dot{\rho}_{97} = i \rho_{912} \Omega{\left(12,7,0 \right)} + i \rho_{916} \Omega{\left(16,7,0 \right)} + i \rho_{922} \Omega{\left(22,7,0 \right)} - i \rho_{97} \Delta{\left(9,7,\omega_{q},v_{z} \right)} - \frac{\rho_{97}}{2 \tau}$

$\displaystyle \dot{\rho}_{98} = i \rho_{917} \Omega{\left(17,8,0 \right)} + i \rho_{923} \Omega{\left(23,8,0 \right)} - i \rho_{98} \Delta{\left(9,8,\omega_{q},v_{z} \right)} - \frac{\rho_{98}}{2 \tau}$

$\displaystyle \dot{\rho}_{101} = - i \rho_{101} \Delta{\left(10,1,\omega_{q},v_{z} \right)} - \frac{\rho_{101}}{2 \tau} + i \rho_{1010} \Omega{\left(10,1,0 \right)} + i \rho_{1014} \Omega{\left(14,1,0 \right)} + i \rho_{11} \Omega{\left(10,1,0 \right)} + i \rho_{21} \Omega{\left(10,1,0 \right)} + i \rho_{31} \Omega{\left(10,1,0 \right)} + i \rho_{41} \Omega{\left(10,1,0 \right)} + i \rho_{51} \Omega{\left(10,1,0 \right)} + i \rho_{61} \Omega{\left(10,1,0 \right)} + i \rho_{71} \Omega{\left(10,1,0 \right)} + i \rho_{81} \Omega{\left(10,1,0 \right)}$

$\displaystyle \dot{\rho}_{102} = i \rho_{1015} \Omega{\left(15,2,0 \right)} - i \rho_{102} \Delta{\left(10,2,\omega_{q},v_{z} \right)} - \frac{\rho_{102}}{2 \tau} + i \rho_{109} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{103} = i \rho_{1012} \Omega{\left(12,3,0 \right)} + i \rho_{1016} \Omega{\left(16,3,0 \right)} - i \rho_{103} \Delta{\left(10,3,\omega_{q},v_{z} \right)} - \frac{\rho_{103}}{2 \tau}$

$\displaystyle \dot{\rho}_{104} = i \rho_{1013} \Omega{\left(13,4,0 \right)} + i \rho_{1019} \Omega{\left(19,4,0 \right)} - i \rho_{104} \Delta{\left(10,4,\omega_{q},v_{z} \right)} - \frac{\rho_{104}}{2 \tau}$

$\displaystyle \dot{\rho}_{105} = i \rho_{1010} \Omega{\left(10,5,0 \right)} + i \rho_{1014} \Omega{\left(14,5,0 \right)} + i \rho_{1020} \Omega{\left(20,5,0 \right)} - i \rho_{105} \Delta{\left(10,5,\omega_{q},v_{z} \right)} - \frac{\rho_{105}}{2 \tau} + i \rho_{15} \Omega{\left(10,5,0 \right)} + i \rho_{25} \Omega{\left(10,5,0 \right)} + i \rho_{35} \Omega{\left(10,5,0 \right)} + i \rho_{45} \Omega{\left(10,5,0 \right)} + i \rho_{55} \Omega{\left(10,5,0 \right)} + i \rho_{65} \Omega{\left(10,5,0 \right)} + i \rho_{75} \Omega{\left(10,5,0 \right)} + i \rho_{85} \Omega{\left(10,5,0 \right)}$

$\displaystyle \dot{\rho}_{106} = i \rho_{1011} \Omega{\left(11,6,0 \right)} + i \rho_{1021} \Omega{\left(21,6,0 \right)} - i \rho_{106} \Delta{\left(10,6,\omega_{q},v_{z} \right)} - \frac{\rho_{106}}{2 \tau}$

$\displaystyle \dot{\rho}_{107} = i \rho_{1012} \Omega{\left(12,7,0 \right)} + i \rho_{1016} \Omega{\left(16,7,0 \right)} + i \rho_{1022} \Omega{\left(22,7,0 \right)} - i \rho_{107} \Delta{\left(10,7,\omega_{q},v_{z} \right)} - \frac{\rho_{107}}{2 \tau}$

$\displaystyle \dot{\rho}_{108} = i \rho_{1017} \Omega{\left(17,8,0 \right)} + i \rho_{1023} \Omega{\left(23,8,0 \right)} - i \rho_{108} \Delta{\left(10,8,\omega_{q},v_{z} \right)} - \frac{\rho_{108}}{2 \tau}$

$\displaystyle \dot{\rho}_{111} = - i \rho_{111} \Delta{\left(11,1,\omega_{q},v_{z} \right)} - \frac{\rho_{111}}{2 \tau} + i \rho_{1110} \Omega{\left(10,1,0 \right)} + i \rho_{1114} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{112} = i \rho_{1115} \Omega{\left(15,2,0 \right)} - i \rho_{112} \Delta{\left(11,2,\omega_{q},v_{z} \right)} - \frac{\rho_{112}}{2 \tau} + i \rho_{119} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{113} = i \rho_{1112} \Omega{\left(12,3,0 \right)} + i \rho_{1116} \Omega{\left(16,3,0 \right)} - i \rho_{113} \Delta{\left(11,3,\omega_{q},v_{z} \right)} - \frac{\rho_{113}}{2 \tau}$

$\displaystyle \dot{\rho}_{114} = i \rho_{1113} \Omega{\left(13,4,0 \right)} + i \rho_{1119} \Omega{\left(19,4,0 \right)} - i \rho_{114} \Delta{\left(11,4,\omega_{q},v_{z} \right)} - \frac{\rho_{114}}{2 \tau}$

$\displaystyle \dot{\rho}_{115} = i \rho_{1110} \Omega{\left(10,5,0 \right)} + i \rho_{1114} \Omega{\left(14,5,0 \right)} + i \rho_{1120} \Omega{\left(20,5,0 \right)} - i \rho_{115} \Delta{\left(11,5,\omega_{q},v_{z} \right)} - \frac{\rho_{115}}{2 \tau}$

$\displaystyle \dot{\rho}_{116} = i \rho_{1111} \Omega{\left(11,6,0 \right)} + i \rho_{1121} \Omega{\left(21,6,0 \right)} - i \rho_{116} \Delta{\left(11,6,\omega_{q},v_{z} \right)} - \frac{\rho_{116}}{2 \tau} + i \rho_{16} \Omega{\left(11,6,0 \right)} + i \rho_{26} \Omega{\left(11,6,0 \right)} + i \rho_{36} \Omega{\left(11,6,0 \right)} + i \rho_{46} \Omega{\left(11,6,0 \right)} + i \rho_{56} \Omega{\left(11,6,0 \right)} + i \rho_{66} \Omega{\left(11,6,0 \right)} + i \rho_{76} \Omega{\left(11,6,0 \right)} + i \rho_{86} \Omega{\left(11,6,0 \right)}$

$\displaystyle \dot{\rho}_{117} = i \rho_{1112} \Omega{\left(12,7,0 \right)} + i \rho_{1116} \Omega{\left(16,7,0 \right)} + i \rho_{1122} \Omega{\left(22,7,0 \right)} - i \rho_{117} \Delta{\left(11,7,\omega_{q},v_{z} \right)} - \frac{\rho_{117}}{2 \tau}$

$\displaystyle \dot{\rho}_{118} = i \rho_{1117} \Omega{\left(17,8,0 \right)} + i \rho_{1123} \Omega{\left(23,8,0 \right)} - i \rho_{118} \Delta{\left(11,8,\omega_{q},v_{z} \right)} - \frac{\rho_{118}}{2 \tau}$

$\displaystyle \dot{\rho}_{121} = - i \rho_{121} \Delta{\left(12,1,\omega_{q},v_{z} \right)} - \frac{\rho_{121}}{2 \tau} + i \rho_{1210} \Omega{\left(10,1,0 \right)} + i \rho_{1214} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{122} = i \rho_{1215} \Omega{\left(15,2,0 \right)} - i \rho_{122} \Delta{\left(12,2,\omega_{q},v_{z} \right)} - \frac{\rho_{122}}{2 \tau} + i \rho_{129} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{123} = i \rho_{1212} \Omega{\left(12,3,0 \right)} + i \rho_{1216} \Omega{\left(16,3,0 \right)} - i \rho_{123} \Delta{\left(12,3,\omega_{q},v_{z} \right)} - \frac{\rho_{123}}{2 \tau} + i \rho_{13} \Omega{\left(12,3,0 \right)} + i \rho_{23} \Omega{\left(12,3,0 \right)} + i \rho_{33} \Omega{\left(12,3,0 \right)} + i \rho_{43} \Omega{\left(12,3,0 \right)} + i \rho_{53} \Omega{\left(12,3,0 \right)} + i \rho_{63} \Omega{\left(12,3,0 \right)} + i \rho_{73} \Omega{\left(12,3,0 \right)} + i \rho_{83} \Omega{\left(12,3,0 \right)}$

$\displaystyle \dot{\rho}_{124} = i \rho_{1213} \Omega{\left(13,4,0 \right)} + i \rho_{1219} \Omega{\left(19,4,0 \right)} - i \rho_{124} \Delta{\left(12,4,\omega_{q},v_{z} \right)} - \frac{\rho_{124}}{2 \tau}$

$\displaystyle \dot{\rho}_{125} = i \rho_{1210} \Omega{\left(10,5,0 \right)} + i \rho_{1214} \Omega{\left(14,5,0 \right)} + i \rho_{1220} \Omega{\left(20,5,0 \right)} - i \rho_{125} \Delta{\left(12,5,\omega_{q},v_{z} \right)} - \frac{\rho_{125}}{2 \tau}$

$\displaystyle \dot{\rho}_{126} = i \rho_{1211} \Omega{\left(11,6,0 \right)} + i \rho_{1221} \Omega{\left(21,6,0 \right)} - i \rho_{126} \Delta{\left(12,6,\omega_{q},v_{z} \right)} - \frac{\rho_{126}}{2 \tau}$

$\displaystyle \dot{\rho}_{127} = i \rho_{1212} \Omega{\left(12,7,0 \right)} + i \rho_{1216} \Omega{\left(16,7,0 \right)} + i \rho_{1222} \Omega{\left(22,7,0 \right)} - i \rho_{127} \Delta{\left(12,7,\omega_{q},v_{z} \right)} - \frac{\rho_{127}}{2 \tau} + i \rho_{17} \Omega{\left(12,7,0 \right)} + i \rho_{27} \Omega{\left(12,7,0 \right)} + i \rho_{37} \Omega{\left(12,7,0 \right)} + i \rho_{47} \Omega{\left(12,7,0 \right)} + i \rho_{57} \Omega{\left(12,7,0 \right)} + i \rho_{67} \Omega{\left(12,7,0 \right)} + i \rho_{77} \Omega{\left(12,7,0 \right)} + i \rho_{87} \Omega{\left(12,7,0 \right)}$

$\displaystyle \dot{\rho}_{128} = i \rho_{1217} \Omega{\left(17,8,0 \right)} + i \rho_{1223} \Omega{\left(23,8,0 \right)} - i \rho_{128} \Delta{\left(12,8,\omega_{q},v_{z} \right)} - \frac{\rho_{128}}{2 \tau}$

$\displaystyle \dot{\rho}_{131} = - i \rho_{131} \Delta{\left(13,1,\omega_{q},v_{z} \right)} - \frac{\rho_{131}}{2 \tau} + i \rho_{1310} \Omega{\left(10,1,0 \right)} + i \rho_{1314} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{132} = i \rho_{1315} \Omega{\left(15,2,0 \right)} - i \rho_{132} \Delta{\left(13,2,\omega_{q},v_{z} \right)} - \frac{\rho_{132}}{2 \tau} + i \rho_{139} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{133} = i \rho_{1312} \Omega{\left(12,3,0 \right)} + i \rho_{1316} \Omega{\left(16,3,0 \right)} - i \rho_{133} \Delta{\left(13,3,\omega_{q},v_{z} \right)} - \frac{\rho_{133}}{2 \tau}$

$\displaystyle \dot{\rho}_{134} = i \rho_{1313} \Omega{\left(13,4,0 \right)} + i \rho_{1319} \Omega{\left(19,4,0 \right)} - i \rho_{134} \Delta{\left(13,4,\omega_{q},v_{z} \right)} - \frac{\rho_{134}}{2 \tau} + i \rho_{14} \Omega{\left(13,4,0 \right)} + i \rho_{24} \Omega{\left(13,4,0 \right)} + i \rho_{34} \Omega{\left(13,4,0 \right)} + i \rho_{44} \Omega{\left(13,4,0 \right)} + i \rho_{54} \Omega{\left(13,4,0 \right)} + i \rho_{64} \Omega{\left(13,4,0 \right)} + i \rho_{74} \Omega{\left(13,4,0 \right)} + i \rho_{84} \Omega{\left(13,4,0 \right)}$

$\displaystyle \dot{\rho}_{135} = i \rho_{1310} \Omega{\left(10,5,0 \right)} + i \rho_{1314} \Omega{\left(14,5,0 \right)} + i \rho_{1320} \Omega{\left(20,5,0 \right)} - i \rho_{135} \Delta{\left(13,5,\omega_{q},v_{z} \right)} - \frac{\rho_{135}}{2 \tau}$

$\displaystyle \dot{\rho}_{136} = i \rho_{1311} \Omega{\left(11,6,0 \right)} + i \rho_{1321} \Omega{\left(21,6,0 \right)} - i \rho_{136} \Delta{\left(13,6,\omega_{q},v_{z} \right)} - \frac{\rho_{136}}{2 \tau}$

$\displaystyle \dot{\rho}_{137} = i \rho_{1312} \Omega{\left(12,7,0 \right)} + i \rho_{1316} \Omega{\left(16,7,0 \right)} + i \rho_{1322} \Omega{\left(22,7,0 \right)} - i \rho_{137} \Delta{\left(13,7,\omega_{q},v_{z} \right)} - \frac{\rho_{137}}{2 \tau}$

$\displaystyle \dot{\rho}_{138} = i \rho_{1317} \Omega{\left(17,8,0 \right)} + i \rho_{1323} \Omega{\left(23,8,0 \right)} - i \rho_{138} \Delta{\left(13,8,\omega_{q},v_{z} \right)} - \frac{\rho_{138}}{2 \tau}$

$\displaystyle \dot{\rho}_{141} = i \rho_{11} \Omega{\left(14,1,0 \right)} - i \rho_{141} \Delta{\left(14,1,\omega_{q},v_{z} \right)} - \frac{\rho_{141}}{2 \tau} + i \rho_{1410} \Omega{\left(10,1,0 \right)} + i \rho_{1414} \Omega{\left(14,1,0 \right)} + i \rho_{21} \Omega{\left(14,1,0 \right)} + i \rho_{31} \Omega{\left(14,1,0 \right)} + i \rho_{41} \Omega{\left(14,1,0 \right)} + i \rho_{51} \Omega{\left(14,1,0 \right)} + i \rho_{61} \Omega{\left(14,1,0 \right)} + i \rho_{71} \Omega{\left(14,1,0 \right)} + i \rho_{81} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{142} = i \rho_{1415} \Omega{\left(15,2,0 \right)} - i \rho_{142} \Delta{\left(14,2,\omega_{q},v_{z} \right)} - \frac{\rho_{142}}{2 \tau} + i \rho_{149} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{143} = i \rho_{1412} \Omega{\left(12,3,0 \right)} + i \rho_{1416} \Omega{\left(16,3,0 \right)} - i \rho_{143} \Delta{\left(14,3,\omega_{q},v_{z} \right)} - \frac{\rho_{143}}{2 \tau}$

$\displaystyle \dot{\rho}_{144} = i \rho_{1413} \Omega{\left(13,4,0 \right)} + i \rho_{1419} \Omega{\left(19,4,0 \right)} - i \rho_{144} \Delta{\left(14,4,\omega_{q},v_{z} \right)} - \frac{\rho_{144}}{2 \tau}$

$\displaystyle \dot{\rho}_{145} = i \rho_{1410} \Omega{\left(10,5,0 \right)} + i \rho_{1414} \Omega{\left(14,5,0 \right)} + i \rho_{1420} \Omega{\left(20,5,0 \right)} - i \rho_{145} \Delta{\left(14,5,\omega_{q},v_{z} \right)} - \frac{\rho_{145}}{2 \tau} + i \rho_{15} \Omega{\left(14,5,0 \right)} + i \rho_{25} \Omega{\left(14,5,0 \right)} + i \rho_{35} \Omega{\left(14,5,0 \right)} + i \rho_{45} \Omega{\left(14,5,0 \right)} + i \rho_{55} \Omega{\left(14,5,0 \right)} + i \rho_{65} \Omega{\left(14,5,0 \right)} + i \rho_{75} \Omega{\left(14,5,0 \right)} + i \rho_{85} \Omega{\left(14,5,0 \right)}$

$\displaystyle \dot{\rho}_{146} = i \rho_{1411} \Omega{\left(11,6,0 \right)} + i \rho_{1421} \Omega{\left(21,6,0 \right)} - i \rho_{146} \Delta{\left(14,6,\omega_{q},v_{z} \right)} - \frac{\rho_{146}}{2 \tau}$

$\displaystyle \dot{\rho}_{147} = i \rho_{1412} \Omega{\left(12,7,0 \right)} + i \rho_{1416} \Omega{\left(16,7,0 \right)} + i \rho_{1422} \Omega{\left(22,7,0 \right)} - i \rho_{147} \Delta{\left(14,7,\omega_{q},v_{z} \right)} - \frac{\rho_{147}}{2 \tau}$

$\displaystyle \dot{\rho}_{148} = i \rho_{1417} \Omega{\left(17,8,0 \right)} + i \rho_{1423} \Omega{\left(23,8,0 \right)} - i \rho_{148} \Delta{\left(14,8,\omega_{q},v_{z} \right)} - \frac{\rho_{148}}{2 \tau}$

$\displaystyle \dot{\rho}_{151} = - i \rho_{151} \Delta{\left(15,1,\omega_{q},v_{z} \right)} - \frac{\rho_{151}}{2 \tau} + i \rho_{1510} \Omega{\left(10,1,0 \right)} + i \rho_{1514} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{152} = i \rho_{12} \Omega{\left(15,2,0 \right)} + i \rho_{1515} \Omega{\left(15,2,0 \right)} - i \rho_{152} \Delta{\left(15,2,\omega_{q},v_{z} \right)} - \frac{\rho_{152}}{2 \tau} + i \rho_{159} \Omega{\left(9,2,0 \right)} + i \rho_{22} \Omega{\left(15,2,0 \right)} + i \rho_{32} \Omega{\left(15,2,0 \right)} + i \rho_{42} \Omega{\left(15,2,0 \right)} + i \rho_{52} \Omega{\left(15,2,0 \right)} + i \rho_{62} \Omega{\left(15,2,0 \right)} + i \rho_{72} \Omega{\left(15,2,0 \right)} + i \rho_{82} \Omega{\left(15,2,0 \right)}$

$\displaystyle \dot{\rho}_{153} = i \rho_{1512} \Omega{\left(12,3,0 \right)} + i \rho_{1516} \Omega{\left(16,3,0 \right)} - i \rho_{153} \Delta{\left(15,3,\omega_{q},v_{z} \right)} - \frac{\rho_{153}}{2 \tau}$

$\displaystyle \dot{\rho}_{154} = i \rho_{1513} \Omega{\left(13,4,0 \right)} + i \rho_{1519} \Omega{\left(19,4,0 \right)} - i \rho_{154} \Delta{\left(15,4,\omega_{q},v_{z} \right)} - \frac{\rho_{154}}{2 \tau}$

$\displaystyle \dot{\rho}_{155} = i \rho_{1510} \Omega{\left(10,5,0 \right)} + i \rho_{1514} \Omega{\left(14,5,0 \right)} + i \rho_{1520} \Omega{\left(20,5,0 \right)} - i \rho_{155} \Delta{\left(15,5,\omega_{q},v_{z} \right)} - \frac{\rho_{155}}{2 \tau}$

$\displaystyle \dot{\rho}_{156} = i \rho_{1511} \Omega{\left(11,6,0 \right)} + i \rho_{1521} \Omega{\left(21,6,0 \right)} - i \rho_{156} \Delta{\left(15,6,\omega_{q},v_{z} \right)} - \frac{\rho_{156}}{2 \tau}$

$\displaystyle \dot{\rho}_{157} = i \rho_{1512} \Omega{\left(12,7,0 \right)} + i \rho_{1516} \Omega{\left(16,7,0 \right)} + i \rho_{1522} \Omega{\left(22,7,0 \right)} - i \rho_{157} \Delta{\left(15,7,\omega_{q},v_{z} \right)} - \frac{\rho_{157}}{2 \tau}$

$\displaystyle \dot{\rho}_{158} = i \rho_{1517} \Omega{\left(17,8,0 \right)} + i \rho_{1523} \Omega{\left(23,8,0 \right)} - i \rho_{158} \Delta{\left(15,8,\omega_{q},v_{z} \right)} - \frac{\rho_{158}}{2 \tau}$

$\displaystyle \dot{\rho}_{161} = - i \rho_{161} \Delta{\left(16,1,\omega_{q},v_{z} \right)} - \frac{\rho_{161}}{2 \tau} + i \rho_{1610} \Omega{\left(10,1,0 \right)} + i \rho_{1614} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{162} = i \rho_{1615} \Omega{\left(15,2,0 \right)} - i \rho_{162} \Delta{\left(16,2,\omega_{q},v_{z} \right)} - \frac{\rho_{162}}{2 \tau} + i \rho_{169} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{163} = i \rho_{13} \Omega{\left(16,3,0 \right)} + i \rho_{1612} \Omega{\left(12,3,0 \right)} + i \rho_{1616} \Omega{\left(16,3,0 \right)} - i \rho_{163} \Delta{\left(16,3,\omega_{q},v_{z} \right)} - \frac{\rho_{163}}{2 \tau} + i \rho_{23} \Omega{\left(16,3,0 \right)} + i \rho_{33} \Omega{\left(16,3,0 \right)} + i \rho_{43} \Omega{\left(16,3,0 \right)} + i \rho_{53} \Omega{\left(16,3,0 \right)} + i \rho_{63} \Omega{\left(16,3,0 \right)} + i \rho_{73} \Omega{\left(16,3,0 \right)} + i \rho_{83} \Omega{\left(16,3,0 \right)}$

$\displaystyle \dot{\rho}_{164} = i \rho_{1613} \Omega{\left(13,4,0 \right)} + i \rho_{1619} \Omega{\left(19,4,0 \right)} - i \rho_{164} \Delta{\left(16,4,\omega_{q},v_{z} \right)} - \frac{\rho_{164}}{2 \tau}$

$\displaystyle \dot{\rho}_{165} = i \rho_{1610} \Omega{\left(10,5,0 \right)} + i \rho_{1614} \Omega{\left(14,5,0 \right)} + i \rho_{1620} \Omega{\left(20,5,0 \right)} - i \rho_{165} \Delta{\left(16,5,\omega_{q},v_{z} \right)} - \frac{\rho_{165}}{2 \tau}$

$\displaystyle \dot{\rho}_{166} = i \rho_{1611} \Omega{\left(11,6,0 \right)} + i \rho_{1621} \Omega{\left(21,6,0 \right)} - i \rho_{166} \Delta{\left(16,6,\omega_{q},v_{z} \right)} - \frac{\rho_{166}}{2 \tau}$

$\displaystyle \dot{\rho}_{167} = i \rho_{1612} \Omega{\left(12,7,0 \right)} + i \rho_{1616} \Omega{\left(16,7,0 \right)} + i \rho_{1622} \Omega{\left(22,7,0 \right)} - i \rho_{167} \Delta{\left(16,7,\omega_{q},v_{z} \right)} - \frac{\rho_{167}}{2 \tau} + i \rho_{17} \Omega{\left(16,7,0 \right)} + i \rho_{27} \Omega{\left(16,7,0 \right)} + i \rho_{37} \Omega{\left(16,7,0 \right)} + i \rho_{47} \Omega{\left(16,7,0 \right)} + i \rho_{57} \Omega{\left(16,7,0 \right)} + i \rho_{67} \Omega{\left(16,7,0 \right)} + i \rho_{77} \Omega{\left(16,7,0 \right)} + i \rho_{87} \Omega{\left(16,7,0 \right)}$

$\displaystyle \dot{\rho}_{168} = i \rho_{1617} \Omega{\left(17,8,0 \right)} + i \rho_{1623} \Omega{\left(23,8,0 \right)} - i \rho_{168} \Delta{\left(16,8,\omega_{q},v_{z} \right)} - \frac{\rho_{168}}{2 \tau}$

$\displaystyle \dot{\rho}_{171} = - i \rho_{171} \Delta{\left(17,1,\omega_{q},v_{z} \right)} - \frac{\rho_{171}}{2 \tau} + i \rho_{1710} \Omega{\left(10,1,0 \right)} + i \rho_{1714} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{172} = i \rho_{1715} \Omega{\left(15,2,0 \right)} - i \rho_{172} \Delta{\left(17,2,\omega_{q},v_{z} \right)} - \frac{\rho_{172}}{2 \tau} + i \rho_{179} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{173} = i \rho_{1712} \Omega{\left(12,3,0 \right)} + i \rho_{1716} \Omega{\left(16,3,0 \right)} - i \rho_{173} \Delta{\left(17,3,\omega_{q},v_{z} \right)} - \frac{\rho_{173}}{2 \tau}$

$\displaystyle \dot{\rho}_{174} = i \rho_{1713} \Omega{\left(13,4,0 \right)} + i \rho_{1719} \Omega{\left(19,4,0 \right)} - i \rho_{174} \Delta{\left(17,4,\omega_{q},v_{z} \right)} - \frac{\rho_{174}}{2 \tau}$

$\displaystyle \dot{\rho}_{175} = i \rho_{1710} \Omega{\left(10,5,0 \right)} + i \rho_{1714} \Omega{\left(14,5,0 \right)} + i \rho_{1720} \Omega{\left(20,5,0 \right)} - i \rho_{175} \Delta{\left(17,5,\omega_{q},v_{z} \right)} - \frac{\rho_{175}}{2 \tau}$

$\displaystyle \dot{\rho}_{176} = i \rho_{1711} \Omega{\left(11,6,0 \right)} + i \rho_{1721} \Omega{\left(21,6,0 \right)} - i \rho_{176} \Delta{\left(17,6,\omega_{q},v_{z} \right)} - \frac{\rho_{176}}{2 \tau}$

$\displaystyle \dot{\rho}_{177} = i \rho_{1712} \Omega{\left(12,7,0 \right)} + i \rho_{1716} \Omega{\left(16,7,0 \right)} + i \rho_{1722} \Omega{\left(22,7,0 \right)} - i \rho_{177} \Delta{\left(17,7,\omega_{q},v_{z} \right)} - \frac{\rho_{177}}{2 \tau}$

$\displaystyle \dot{\rho}_{178} = i \rho_{1717} \Omega{\left(17,8,0 \right)} + i \rho_{1723} \Omega{\left(23,8,0 \right)} - i \rho_{178} \Delta{\left(17,8,\omega_{q},v_{z} \right)} - \frac{\rho_{178}}{2 \tau} + i \rho_{18} \Omega{\left(17,8,0 \right)} + i \rho_{28} \Omega{\left(17,8,0 \right)} + i \rho_{38} \Omega{\left(17,8,0 \right)} + i \rho_{48} \Omega{\left(17,8,0 \right)} + i \rho_{58} \Omega{\left(17,8,0 \right)} + i \rho_{68} \Omega{\left(17,8,0 \right)} + i \rho_{78} \Omega{\left(17,8,0 \right)} + i \rho_{88} \Omega{\left(17,8,0 \right)}$

$\displaystyle \dot{\rho}_{181} = - i \rho_{181} \Delta{\left(18,1,\omega_{q},v_{z} \right)} - \frac{\rho_{181}}{2 \tau} + i \rho_{1810} \Omega{\left(10,1,0 \right)} + i \rho_{1814} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{182} = i \rho_{1815} \Omega{\left(15,2,0 \right)} - i \rho_{182} \Delta{\left(18,2,\omega_{q},v_{z} \right)} - \frac{\rho_{182}}{2 \tau} + i \rho_{189} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{183} = i \rho_{1812} \Omega{\left(12,3,0 \right)} + i \rho_{1816} \Omega{\left(16,3,0 \right)} - i \rho_{183} \Delta{\left(18,3,\omega_{q},v_{z} \right)} - \frac{\rho_{183}}{2 \tau}$

$\displaystyle \dot{\rho}_{184} = i \rho_{1813} \Omega{\left(13,4,0 \right)} + i \rho_{1819} \Omega{\left(19,4,0 \right)} - i \rho_{184} \Delta{\left(18,4,\omega_{q},v_{z} \right)} - \frac{\rho_{184}}{2 \tau}$

$\displaystyle \dot{\rho}_{185} = i \rho_{1810} \Omega{\left(10,5,0 \right)} + i \rho_{1814} \Omega{\left(14,5,0 \right)} + i \rho_{1820} \Omega{\left(20,5,0 \right)} - i \rho_{185} \Delta{\left(18,5,\omega_{q},v_{z} \right)} - \frac{\rho_{185}}{2 \tau}$

$\displaystyle \dot{\rho}_{186} = i \rho_{1811} \Omega{\left(11,6,0 \right)} + i \rho_{1821} \Omega{\left(21,6,0 \right)} - i \rho_{186} \Delta{\left(18,6,\omega_{q},v_{z} \right)} - \frac{\rho_{186}}{2 \tau}$

$\displaystyle \dot{\rho}_{187} = i \rho_{1812} \Omega{\left(12,7,0 \right)} + i \rho_{1816} \Omega{\left(16,7,0 \right)} + i \rho_{1822} \Omega{\left(22,7,0 \right)} - i \rho_{187} \Delta{\left(18,7,\omega_{q},v_{z} \right)} - \frac{\rho_{187}}{2 \tau}$

$\displaystyle \dot{\rho}_{188} = i \rho_{1817} \Omega{\left(17,8,0 \right)} + i \rho_{1823} \Omega{\left(23,8,0 \right)} - i \rho_{188} \Delta{\left(18,8,\omega_{q},v_{z} \right)} - \frac{\rho_{188}}{2 \tau}$

$\displaystyle \dot{\rho}_{191} = - i \rho_{191} \Delta{\left(19,1,\omega_{q},v_{z} \right)} - \frac{\rho_{191}}{2 \tau} + i \rho_{1910} \Omega{\left(10,1,0 \right)} + i \rho_{1914} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{192} = i \rho_{1915} \Omega{\left(15,2,0 \right)} - i \rho_{192} \Delta{\left(19,2,\omega_{q},v_{z} \right)} - \frac{\rho_{192}}{2 \tau} + i \rho_{199} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{193} = i \rho_{1912} \Omega{\left(12,3,0 \right)} + i \rho_{1916} \Omega{\left(16,3,0 \right)} - i \rho_{193} \Delta{\left(19,3,\omega_{q},v_{z} \right)} - \frac{\rho_{193}}{2 \tau}$

$\displaystyle \dot{\rho}_{194} = i \rho_{14} \Omega{\left(19,4,0 \right)} + i \rho_{1913} \Omega{\left(13,4,0 \right)} + i \rho_{1919} \Omega{\left(19,4,0 \right)} - i \rho_{194} \Delta{\left(19,4,\omega_{q},v_{z} \right)} - \frac{\rho_{194}}{2 \tau} + i \rho_{24} \Omega{\left(19,4,0 \right)} + i \rho_{34} \Omega{\left(19,4,0 \right)} + i \rho_{44} \Omega{\left(19,4,0 \right)} + i \rho_{54} \Omega{\left(19,4,0 \right)} + i \rho_{64} \Omega{\left(19,4,0 \right)} + i \rho_{74} \Omega{\left(19,4,0 \right)} + i \rho_{84} \Omega{\left(19,4,0 \right)}$

$\displaystyle \dot{\rho}_{195} = i \rho_{1910} \Omega{\left(10,5,0 \right)} + i \rho_{1914} \Omega{\left(14,5,0 \right)} + i \rho_{1920} \Omega{\left(20,5,0 \right)} - i \rho_{195} \Delta{\left(19,5,\omega_{q},v_{z} \right)} - \frac{\rho_{195}}{2 \tau}$

$\displaystyle \dot{\rho}_{196} = i \rho_{1911} \Omega{\left(11,6,0 \right)} + i \rho_{1921} \Omega{\left(21,6,0 \right)} - i \rho_{196} \Delta{\left(19,6,\omega_{q},v_{z} \right)} - \frac{\rho_{196}}{2 \tau}$

$\displaystyle \dot{\rho}_{197} = i \rho_{1912} \Omega{\left(12,7,0 \right)} + i \rho_{1916} \Omega{\left(16,7,0 \right)} + i \rho_{1922} \Omega{\left(22,7,0 \right)} - i \rho_{197} \Delta{\left(19,7,\omega_{q},v_{z} \right)} - \frac{\rho_{197}}{2 \tau}$

$\displaystyle \dot{\rho}_{198} = i \rho_{1917} \Omega{\left(17,8,0 \right)} + i \rho_{1923} \Omega{\left(23,8,0 \right)} - i \rho_{198} \Delta{\left(19,8,\omega_{q},v_{z} \right)} - \frac{\rho_{198}}{2 \tau}$

$\displaystyle \dot{\rho}_{201} = - i \rho_{201} \Delta{\left(20,1,\omega_{q},v_{z} \right)} - \frac{\rho_{201}}{2 \tau} + i \rho_{2010} \Omega{\left(10,1,0 \right)} + i \rho_{2014} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{202} = i \rho_{2015} \Omega{\left(15,2,0 \right)} - i \rho_{202} \Delta{\left(20,2,\omega_{q},v_{z} \right)} - \frac{\rho_{202}}{2 \tau} + i \rho_{209} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{203} = i \rho_{2012} \Omega{\left(12,3,0 \right)} + i \rho_{2016} \Omega{\left(16,3,0 \right)} - i \rho_{203} \Delta{\left(20,3,\omega_{q},v_{z} \right)} - \frac{\rho_{203}}{2 \tau}$

$\displaystyle \dot{\rho}_{204} = i \rho_{2013} \Omega{\left(13,4,0 \right)} + i \rho_{2019} \Omega{\left(19,4,0 \right)} - i \rho_{204} \Delta{\left(20,4,\omega_{q},v_{z} \right)} - \frac{\rho_{204}}{2 \tau}$

$\displaystyle \dot{\rho}_{205} = i \rho_{15} \Omega{\left(20,5,0 \right)} + i \rho_{2010} \Omega{\left(10,5,0 \right)} + i \rho_{2014} \Omega{\left(14,5,0 \right)} + i \rho_{2020} \Omega{\left(20,5,0 \right)} - i \rho_{205} \Delta{\left(20,5,\omega_{q},v_{z} \right)} - \frac{\rho_{205}}{2 \tau} + i \rho_{25} \Omega{\left(20,5,0 \right)} + i \rho_{35} \Omega{\left(20,5,0 \right)} + i \rho_{45} \Omega{\left(20,5,0 \right)} + i \rho_{55} \Omega{\left(20,5,0 \right)} + i \rho_{65} \Omega{\left(20,5,0 \right)} + i \rho_{75} \Omega{\left(20,5,0 \right)} + i \rho_{85} \Omega{\left(20,5,0 \right)}$

$\displaystyle \dot{\rho}_{206} = i \rho_{2011} \Omega{\left(11,6,0 \right)} + i \rho_{2021} \Omega{\left(21,6,0 \right)} - i \rho_{206} \Delta{\left(20,6,\omega_{q},v_{z} \right)} - \frac{\rho_{206}}{2 \tau}$

$\displaystyle \dot{\rho}_{207} = i \rho_{2012} \Omega{\left(12,7,0 \right)} + i \rho_{2016} \Omega{\left(16,7,0 \right)} + i \rho_{2022} \Omega{\left(22,7,0 \right)} - i \rho_{207} \Delta{\left(20,7,\omega_{q},v_{z} \right)} - \frac{\rho_{207}}{2 \tau}$

$\displaystyle \dot{\rho}_{208} = i \rho_{2017} \Omega{\left(17,8,0 \right)} + i \rho_{2023} \Omega{\left(23,8,0 \right)} - i \rho_{208} \Delta{\left(20,8,\omega_{q},v_{z} \right)} - \frac{\rho_{208}}{2 \tau}$

$\displaystyle \dot{\rho}_{211} = - i \rho_{211} \Delta{\left(21,1,\omega_{q},v_{z} \right)} - \frac{\rho_{211}}{2 \tau} + i \rho_{2110} \Omega{\left(10,1,0 \right)} + i \rho_{2114} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{212} = i \rho_{2115} \Omega{\left(15,2,0 \right)} - i \rho_{212} \Delta{\left(21,2,\omega_{q},v_{z} \right)} - \frac{\rho_{212}}{2 \tau} + i \rho_{219} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{213} = i \rho_{2112} \Omega{\left(12,3,0 \right)} + i \rho_{2116} \Omega{\left(16,3,0 \right)} - i \rho_{213} \Delta{\left(21,3,\omega_{q},v_{z} \right)} - \frac{\rho_{213}}{2 \tau}$

$\displaystyle \dot{\rho}_{214} = i \rho_{2113} \Omega{\left(13,4,0 \right)} + i \rho_{2119} \Omega{\left(19,4,0 \right)} - i \rho_{214} \Delta{\left(21,4,\omega_{q},v_{z} \right)} - \frac{\rho_{214}}{2 \tau}$

$\displaystyle \dot{\rho}_{215} = i \rho_{2110} \Omega{\left(10,5,0 \right)} + i \rho_{2114} \Omega{\left(14,5,0 \right)} + i \rho_{2120} \Omega{\left(20,5,0 \right)} - i \rho_{215} \Delta{\left(21,5,\omega_{q},v_{z} \right)} - \frac{\rho_{215}}{2 \tau}$

$\displaystyle \dot{\rho}_{216} = i \rho_{16} \Omega{\left(21,6,0 \right)} + i \rho_{2111} \Omega{\left(11,6,0 \right)} + i \rho_{2121} \Omega{\left(21,6,0 \right)} - i \rho_{216} \Delta{\left(21,6,\omega_{q},v_{z} \right)} - \frac{\rho_{216}}{2 \tau} + i \rho_{26} \Omega{\left(21,6,0 \right)} + i \rho_{36} \Omega{\left(21,6,0 \right)} + i \rho_{46} \Omega{\left(21,6,0 \right)} + i \rho_{56} \Omega{\left(21,6,0 \right)} + i \rho_{66} \Omega{\left(21,6,0 \right)} + i \rho_{76} \Omega{\left(21,6,0 \right)} + i \rho_{86} \Omega{\left(21,6,0 \right)}$

$\displaystyle \dot{\rho}_{217} = i \rho_{2112} \Omega{\left(12,7,0 \right)} + i \rho_{2116} \Omega{\left(16,7,0 \right)} + i \rho_{2122} \Omega{\left(22,7,0 \right)} - i \rho_{217} \Delta{\left(21,7,\omega_{q},v_{z} \right)} - \frac{\rho_{217}}{2 \tau}$

$\displaystyle \dot{\rho}_{218} = i \rho_{2117} \Omega{\left(17,8,0 \right)} + i \rho_{2123} \Omega{\left(23,8,0 \right)} - i \rho_{218} \Delta{\left(21,8,\omega_{q},v_{z} \right)} - \frac{\rho_{218}}{2 \tau}$

$\displaystyle \dot{\rho}_{221} = - i \rho_{221} \Delta{\left(22,1,\omega_{q},v_{z} \right)} - \frac{\rho_{221}}{2 \tau} + i \rho_{2210} \Omega{\left(10,1,0 \right)} + i \rho_{2214} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{222} = i \rho_{2215} \Omega{\left(15,2,0 \right)} - i \rho_{222} \Delta{\left(22,2,\omega_{q},v_{z} \right)} - \frac{\rho_{222}}{2 \tau} + i \rho_{229} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{223} = i \rho_{2212} \Omega{\left(12,3,0 \right)} + i \rho_{2216} \Omega{\left(16,3,0 \right)} - i \rho_{223} \Delta{\left(22,3,\omega_{q},v_{z} \right)} - \frac{\rho_{223}}{2 \tau}$

$\displaystyle \dot{\rho}_{224} = i \rho_{2213} \Omega{\left(13,4,0 \right)} + i \rho_{2219} \Omega{\left(19,4,0 \right)} - i \rho_{224} \Delta{\left(22,4,\omega_{q},v_{z} \right)} - \frac{\rho_{224}}{2 \tau}$

$\displaystyle \dot{\rho}_{225} = i \rho_{2210} \Omega{\left(10,5,0 \right)} + i \rho_{2214} \Omega{\left(14,5,0 \right)} + i \rho_{2220} \Omega{\left(20,5,0 \right)} - i \rho_{225} \Delta{\left(22,5,\omega_{q},v_{z} \right)} - \frac{\rho_{225}}{2 \tau}$

$\displaystyle \dot{\rho}_{226} = i \rho_{2211} \Omega{\left(11,6,0 \right)} + i \rho_{2221} \Omega{\left(21,6,0 \right)} - i \rho_{226} \Delta{\left(22,6,\omega_{q},v_{z} \right)} - \frac{\rho_{226}}{2 \tau}$

$\displaystyle \dot{\rho}_{227} = i \rho_{17} \Omega{\left(22,7,0 \right)} + i \rho_{2212} \Omega{\left(12,7,0 \right)} + i \rho_{2216} \Omega{\left(16,7,0 \right)} + i \rho_{2222} \Omega{\left(22,7,0 \right)} - i \rho_{227} \Delta{\left(22,7,\omega_{q},v_{z} \right)} - \frac{\rho_{227}}{2 \tau} + i \rho_{27} \Omega{\left(22,7,0 \right)} + i \rho_{37} \Omega{\left(22,7,0 \right)} + i \rho_{47} \Omega{\left(22,7,0 \right)} + i \rho_{57} \Omega{\left(22,7,0 \right)} + i \rho_{67} \Omega{\left(22,7,0 \right)} + i \rho_{77} \Omega{\left(22,7,0 \right)} + i \rho_{87} \Omega{\left(22,7,0 \right)}$

$\displaystyle \dot{\rho}_{228} = i \rho_{2217} \Omega{\left(17,8,0 \right)} + i \rho_{2223} \Omega{\left(23,8,0 \right)} - i \rho_{228} \Delta{\left(22,8,\omega_{q},v_{z} \right)} - \frac{\rho_{228}}{2 \tau}$

$\displaystyle \dot{\rho}_{231} = - i \rho_{231} \Delta{\left(23,1,\omega_{q},v_{z} \right)} - \frac{\rho_{231}}{2 \tau} + i \rho_{2310} \Omega{\left(10,1,0 \right)} + i \rho_{2314} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{232} = i \rho_{2315} \Omega{\left(15,2,0 \right)} - i \rho_{232} \Delta{\left(23,2,\omega_{q},v_{z} \right)} - \frac{\rho_{232}}{2 \tau} + i \rho_{239} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{233} = i \rho_{2312} \Omega{\left(12,3,0 \right)} + i \rho_{2316} \Omega{\left(16,3,0 \right)} - i \rho_{233} \Delta{\left(23,3,\omega_{q},v_{z} \right)} - \frac{\rho_{233}}{2 \tau}$

$\displaystyle \dot{\rho}_{234} = i \rho_{2313} \Omega{\left(13,4,0 \right)} + i \rho_{2319} \Omega{\left(19,4,0 \right)} - i \rho_{234} \Delta{\left(23,4,\omega_{q},v_{z} \right)} - \frac{\rho_{234}}{2 \tau}$

$\displaystyle \dot{\rho}_{235} = i \rho_{2310} \Omega{\left(10,5,0 \right)} + i \rho_{2314} \Omega{\left(14,5,0 \right)} + i \rho_{2320} \Omega{\left(20,5,0 \right)} - i \rho_{235} \Delta{\left(23,5,\omega_{q},v_{z} \right)} - \frac{\rho_{235}}{2 \tau}$

$\displaystyle \dot{\rho}_{236} = i \rho_{2311} \Omega{\left(11,6,0 \right)} + i \rho_{2321} \Omega{\left(21,6,0 \right)} - i \rho_{236} \Delta{\left(23,6,\omega_{q},v_{z} \right)} - \frac{\rho_{236}}{2 \tau}$

$\displaystyle \dot{\rho}_{237} = i \rho_{2312} \Omega{\left(12,7,0 \right)} + i \rho_{2316} \Omega{\left(16,7,0 \right)} + i \rho_{2322} \Omega{\left(22,7,0 \right)} - i \rho_{237} \Delta{\left(23,7,\omega_{q},v_{z} \right)} - \frac{\rho_{237}}{2 \tau}$

$\displaystyle \dot{\rho}_{238} = i \rho_{18} \Omega{\left(23,8,0 \right)} + i \rho_{2317} \Omega{\left(17,8,0 \right)} + i \rho_{2323} \Omega{\left(23,8,0 \right)} - i \rho_{238} \Delta{\left(23,8,\omega_{q},v_{z} \right)} - \frac{\rho_{238}}{2 \tau} + i \rho_{28} \Omega{\left(23,8,0 \right)} + i \rho_{38} \Omega{\left(23,8,0 \right)} + i \rho_{48} \Omega{\left(23,8,0 \right)} + i \rho_{58} \Omega{\left(23,8,0 \right)} + i \rho_{68} \Omega{\left(23,8,0 \right)} + i \rho_{78} \Omega{\left(23,8,0 \right)} + i \rho_{88} \Omega{\left(23,8,0 \right)}$

$\displaystyle \dot{\rho}_{241} = - i \rho_{241} \Delta{\left(24,1,\omega_{q},v_{z} \right)} - \frac{\rho_{241}}{2 \tau} + i \rho_{2410} \Omega{\left(10,1,0 \right)} + i \rho_{2414} \Omega{\left(14,1,0 \right)}$

$\displaystyle \dot{\rho}_{242} = i \rho_{2415} \Omega{\left(15,2,0 \right)} - i \rho_{242} \Delta{\left(24,2,\omega_{q},v_{z} \right)} - \frac{\rho_{242}}{2 \tau} + i \rho_{249} \Omega{\left(9,2,0 \right)}$

$\displaystyle \dot{\rho}_{243} = i \rho_{2412} \Omega{\left(12,3,0 \right)} + i \rho_{2416} \Omega{\left(16,3,0 \right)} - i \rho_{243} \Delta{\left(24,3,\omega_{q},v_{z} \right)} - \frac{\rho_{243}}{2 \tau}$

$\displaystyle \dot{\rho}_{244} = i \rho_{2413} \Omega{\left(13,4,0 \right)} + i \rho_{2419} \Omega{\left(19,4,0 \right)} - i \rho_{244} \Delta{\left(24,4,\omega_{q},v_{z} \right)} - \frac{\rho_{244}}{2 \tau}$

$\displaystyle \dot{\rho}_{245} = i \rho_{2410} \Omega{\left(10,5,0 \right)} + i \rho_{2414} \Omega{\left(14,5,0 \right)} + i \rho_{2420} \Omega{\left(20,5,0 \right)} - i \rho_{245} \Delta{\left(24,5,\omega_{q},v_{z} \right)} - \frac{\rho_{245}}{2 \tau}$

$\displaystyle \dot{\rho}_{246} = i \rho_{2411} \Omega{\left(11,6,0 \right)} + i \rho_{2421} \Omega{\left(21,6,0 \right)} - i \rho_{246} \Delta{\left(24,6,\omega_{q},v_{z} \right)} - \frac{\rho_{246}}{2 \tau}$

$\displaystyle \dot{\rho}_{247} = i \rho_{2412} \Omega{\left(12,7,0 \right)} + i \rho_{2416} \Omega{\left(16,7,0 \right)} + i \rho_{2422} \Omega{\left(22,7,0 \right)} - i \rho_{247} \Delta{\left(24,7,\omega_{q},v_{z} \right)} - \frac{\rho_{247}}{2 \tau}$

$\displaystyle \dot{\rho}_{248} = i \rho_{2417} \Omega{\left(17,8,0 \right)} + i \rho_{2423} \Omega{\left(23,8,0 \right)} - i \rho_{248} \Delta{\left(24,8,\omega_{q},v_{z} \right)} - \frac{\rho_{248}}{2 \tau}$

The code finished in 1212.1779 seconds

las_sys = sodium_system

rho_to_plot = [ [abs(rho) for rho in las_sys.Rho_t(s, s)] for s in F0]

fig_na = go.Figure()

for i, rho_ee in enumerate(rho_to_plot):
    fig_na.add_trace(go.Scatter(x = time_na,
                                y = rho_ee,
                                name = f"m_F = {F0[i].m}",
                               mode = 'lines'))

fig_na.update_layout(title = "Sodium F = 0",
                 xaxis_title = "Time (ns)",
                 yaxis_title = "Population",
                font = dict(
                    size = 11))
fig_na.write_image("NaF=0I=856.pdf")
fig_na.show()

las_sys = sodium_system

rho_to_plot = [ [abs(rho) for rho in las_sys.Rho_t(s, s)] for s in F1]

fig_na = go.Figure()

for i, rho_ee in enumerate(rho_to_plot):
    fig_na.add_trace(go.Scatter(x = time_na,
                                y = rho_ee,
                                name = f"m_F = {F1[i].m}",
                               mode = 'lines'))

fig_na.update_layout(title = "Sodium F = 1",
                 xaxis_title = "Time (ns)",
                 yaxis_title = "Population",
                font = dict(
                    size = 11))
fig_na.write_image(f"NaF=1I=856.pdf")
fig_na.show()

las_sys = sodium_system

rho_to_plot = [ [abs(rho) for rho in las_sys.Rho_t(s, s)] for s in F2]

fig_na = go.Figure()

for i, rho_ee in enumerate(rho_to_plot):
    fig_na.add_trace(go.Scatter(x = time_na,
                                y = rho_ee,
                                name = f"m_F = {F2[i].m}",
                               mode = 'lines'))

fig_na.update_layout(title = "Sodium F = 2",
                 xaxis_title = "Time (ns)",
                 yaxis_title = "Population",
                font = dict(
                    size = 11))
fig_na.write_image("NaF=2I=856.pdf")
fig_na.show()

las_sys = sodium_system

rho_to_plot = [ [abs(rho) for rho in las_sys.Rho_t(s, s)] for s in F3]

fig_na = go.Figure()

for i, rho_ee in enumerate(rho_to_plot):
    fig_na.add_trace(go.Scatter(x = time_na,
                                y = rho_ee,
                                name = f"m_F = {F3[i].m}",
                               mode = 'lines'))

fig_na.update_layout(title = "Sodium F = 3",
                 xaxis_title = "Time (ns)",
                 yaxis_title = "Population",
                font = dict(
                    size = 11))
fig_na.write_image("NaF=3I=856.pdf")
fig_na.show()

fig_na_lower = go.Figure()

rho_to_plot = [ [abs(rho) for rho in las_sys.Rho_t(s, s)] for s in Fp1]

for i, rho_gg in enumerate(rho_to_plot):
    fig_na_lower.add_trace(go.Scatter(x = time_na,
                                y = rho_gg,
                                name = f"m_F = {Fp1[i].m}",
                               mode = 'lines'))
fig_na_lower.update_layout(title = "Sodium F' = 1",
                 xaxis_title = "Time (ns)",
                 yaxis_title = "Population",
                font = dict(
                    size = 11))
fig_na.write_image("NaFp=1I=856.pdf")
fig_na_lower.show()

fig_na_lower = go.Figure()

rho_to_plot = [ [abs(rho) for rho in las_sys.Rho_t(s, s)] for s in Fp2]

for i, rho_gg in enumerate(rho_to_plot):
    fig_na_lower.add_trace(go.Scatter(x = time_na,
                                y = rho_gg,
                                name = f"m_F = {Fp2[i].m}",
                               mode = 'lines'))
fig_na_lower.update_layout(title = "Sodium F' = 2",
                 xaxis_title = "Time (ns)",
                 yaxis_title = "Population",
                font = dict(
                    size = 11))
fig_na.write_image("NaFp=2I=856.pdf")
fig_na_lower.show()

# Make subplots
from plotly.subplots import make_subplots

fig = make_subplots(rows = 3, cols = 2, shared_xaxes = True,
                   subplot_titles = ["F = 0", "F = 1"])

# F = 0
rho_to_plot = [ [abs(rho) for rho in las_sys.Rho_t(s, s)] for s in F0]
for i, rho_ee in enumerate(rho_to_plot):
    fig.add_trace(go.Scatter(x = time_na,
                                y = rho_ee,
                                name = f"m_F = {F0[i].m}",
                               mode = 'lines'),
                 row = 1, col = 1)

# F = 1
rho_to_plot = [ [abs(rho) for rho in las_sys.Rho_t(s, s)] for s in F1]
for i, rho_ee in enumerate(rho_to_plot):
    fig.add_trace(go.Scatter(x = time_na,
                                y = rho_ee,
                                name = f"m_F = {F1[i].m}",
                               mode = 'lines'),
                 row = 1, col = 2)
fig['layout'].update(
    annotations=[
    dict(
        x=97, y=498e-6, # annotation point
        xref='x1',
        yref='y1',
        text='m<sub>F</sub>=0',
        showarrow=True,
    ),
#     dict(
#         ...
#         # if have multiple annotations
#     )
])
fig.update_layout(title = "Level Populations of Sodium D-line after Laser Excitation",
                 xaxis_title = "Time (ns)",
                 yaxis_title = "Population",
                font = dict(
                    size = 11))
# fig.add_annotation(x = 97, y = 498e-6, text = "m_F = 0", showarrow = True)
# fig.add_annotation(x2 = 12, y2 = 0.04, text = "m_F = 0", showarrow = True)
fig.show()